Linear period time-varying system output feedback stabilization control design method and device

Abstract

The invention belongs to the technical field of linear system dynamics analysis and control, and particularly discloses a linear period time-varying system output feedback stabilization control design method and device, and the method comprises the steps: obtaining a state transition matrix through a numerical calculation method based on a linear period time-varying system; based on the state transition matrix and a preset new input variable, obtaining a transformed input variable, a transformed output variable and a discrete linear time-invariant system; designing an observer and a state feedback control law based on the discrete linear time-invariant system, the preset new input variable and the transformed output variable; and constructing output feedback stabilization control of the linear period time-varying system based on the transformed input variable, the transformed output variable, the observer, the state feedback control law and the preset new input variable. According to the method, system stabilization can be effectively achieved, strict mathematical conditions and hypotheses do not need to be introduced for solving, the application range is wider, and the method can be applied to a generalized linear period time-varying system.

Description

Technical Field

[0001] This application belongs to the technical field of linear system dynamics analysis and control. More specifically, it relates to a design method and device for output feedback stabilization control of a linear periodic time-varying system. Background Art

[0002] The linear periodic time-varying system model is widely used in practical engineering scenarios such as small-signal stability analysis of power systems, spacecraft flight attitude control, and wind turbine blade vibration analysis. Therefore, its stabilization control is of great significance for ensuring the safe and stable operation of the above-mentioned practical engineering systems.

[0003] The existing stabilization control of linear periodic time-varying systems is mainly divided into two categories: 1) state feedback control; 2) output feedback control. Among them, state feedback control requires information on all states in the system; however, it is difficult to ensure that all state information is observable or measurable in an actual system, which limits the application of state feedback control. And the existing output feedback control design methods mainly include the sampling-period holding method, the optimal control design method, the auxiliary matrix design method, etc. Although the above methods can be used to solve the output feedback control law of linear periodic time-varying systems, they all have certain defects. For example, the sampling-period holding method requires the number of system state variables to be the same as the number of input variables, and it is difficult for a general linear periodic time-varying system to meet this condition; the optimal control design method involves solving complex functional relationships and requires harsh mathematical conditions to ensure the existence of the control law; although the auxiliary matrix design method has a simple calculation process, it can only obtain the control law in the least squares sense and is difficult to ensure the realization of the stabilization function. Therefore, the applicable range of the existing stabilization control methods for linear periodic time-varying systems has limitations. Summary of the Invention

[0004] Aiming at the defects of the existing technology, the purpose of this application is to provide a design method for output feedback stabilization control of a linear periodic time-varying system, aiming to solve the problem that the applicable range of the existing stabilization control methods for linear periodic time-varying systems is limited due to overly strict required conditions.

[0005] To achieve the above object, in a first aspect, this application provides a design method for output feedback stabilization control of a linear periodic time-varying system, including: Based on the linear periodic time-varying system, obtain the state transition matrix through a numerical calculation method; Based on the state transition matrix and a preset new input variable, obtain the transformed input variable, the transformed output variable, and a discrete linear time-invariant system; Based on the discrete linear time-invariant system, the preset new input variable, and the transformed output variable, design an observer and a state feedback control law; Based on the transformed input variable, the transformed output variable, the observer, and the preset new input variable, construct the output feedback stabilization control of the linear periodic time-varying system.

[0006] This application constructs the output feedback stabilization control of the linear periodic time-varying system based on the transformed input variable, the transformed output variable, the observer, the state feedback control law, and the preset new input variable, which can configure the closed-loop system eigenvalues to the desired positions, thereby increasing the damping of the negative damping / weak damping oscillation mode of the linear periodic time-varying system, effectively realizing system stabilization, and the solution does not require introducing strict mathematical conditions and assumptions, with a wider application range and can be applied to general linear periodic time-varying systems.

[0007] According to a design method for output feedback stabilization control of a linear periodic time-varying system provided by this application, the preset new input variable is calculated by the formula where is the preset new input variable in the th period, is a n × n dimensional matrix, and is the observer state in the th period.

[0008] According to a design method for output feedback stabilization control of a linear periodic time-varying system provided by this application, constructing the transformed input variable, the transformed output variable, and the discrete linear time-invariant system based on the state transition matrix and the preset new input variable includes: Construct the transformed input variable as where is the transformed input variable, is the transpose of the t × n × p dimensional input matrix of the linear periodic time-varying system at time is the state transition matrix, is the preset new input variable, is the integer obtained by taking the integer part of t / T and T is the minimum period of the linear periodic time-varying system.

[0009] According to a design method for output feedback stabilization control of a linear periodic time-varying system provided by this application, constructing the transformed input variable, the transformed output variable, and the discrete linear time-invariant system based on the state transition matrix and the preset new input variable includes: Construct the transformed output variable as where is the th The transformed output variable of one period is the state transition matrix is the transpose of the output matrix of the linear periodic time-varying system at time instant is the output variable at is / T the integer after rounding T is the minimum period of the linear periodic time-varying system

[0010] According to a design method for output feedback stabilization control of a linear periodic time-varying system provided by the present application, constructing a transformed input variable, a transformed output variable, and a discrete linear time-invariant system based on the state transition matrix and a preset new input variable includes: Obtaining matrices W r ( T , 0), W o ( T , 0) and W c ( T , 0); Based on the matrix W r ( T , 0), W o ( T , 0) and W c ( T , 0), constructing the discrete linear time-invariant system , where , is the preset new input variable of the th period, is the sampled value of the state variable of the linear periodic time-varying system at time instant, is the transformed output variable of the th period, is the state transition matrix, is the identity matrix

[0011] According to a design method for output feedback stabilization control of a linear periodic time-varying system provided by the present application, designing an observer based on the discrete linear time-invariant system includes: Designing the observer as , where is n × ndimensional matrix, is the preset new input variable for the th cycle, is the transformed output variable for the th cycle, is the observer state for the +1 th cycle, is the observer state for the th cycle.

[0012] In a second aspect, the present application provides a linear periodic time-varying system output feedback stabilization control design device, including: A first acquisition module, configured to obtain a state transition matrix based on a linear periodic time-varying system through a numerical calculation method; A second acquisition module, configured to obtain a transformed input variable, a transformed output variable, and a discrete linear time-invariant system based on the state transition matrix and a preset new input variable; A design module, configured to design an observer and a state feedback control law based on the discrete linear time-invariant system, the preset new input variable, and the transformed output variable; A construction module, configured to construct the output feedback stabilization control of the linear periodic time-varying system based on the transformed input variable, the transformed output variable, the observer, the state feedback control law, and the preset new input variable.

[0013] In a third aspect, the present application provides an electronic device, including: at least one memory for storing a program; at least one processor for executing the program stored in the memory, and when the program stored in the memory is executed, the processor is configured to execute the linear periodic time-varying system output feedback stabilization control design method described in the first aspect or any one of the possible implementation manners of the first aspect.

[0014] In a fourth aspect, the present application provides a computer-readable storage medium storing a computer program, and when the computer program runs on a processor, it causes the processor to execute the linear periodic time-varying system output feedback stabilization control design method described in the first aspect or any one of the possible implementation manners of the first aspect.

[0015] In a fifth aspect, the present application provides a computer program product, and when the computer program product runs on a processor, it causes the processor to execute the linear periodic time-varying system output feedback stabilization control design method described in the first aspect or any one of the possible implementation manners of the first aspect.

[0016] It can be understood that the beneficial effects of the above second aspect to fifth aspect can refer to the relevant descriptions in the above first aspect, and will not be elaborated here.

[0017] Generally speaking, compared with the prior art, the above technical solutions conceived by this application have the following beneficial effects: Based on the transformed input variables, transformed output variables, observer, state feedback control law, and preset new input variables, this application constructs an output feedback stabilization control for a linear periodically time-varying system, which can configure the closed-loop system eigenvalues to the desired positions, thereby increasing the damping of the negative damping / weak damping oscillation modes of the linear periodically time-varying system, effectively realizing system stabilization, and the solution does not require the introduction of stringent mathematical conditions and assumptions, with a wider scope of application, and can be applied to general linear periodically time-varying systems. Description of the Drawings

[0018] To more clearly illustrate the technical solutions in this application or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of this application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0019] Figure 1 is one of the schematic flowcharts of the design method for output feedback stabilization control of a linear periodically time-varying system provided by an embodiment of this application; Figure 2 is the second of the schematic flowcharts of the design method for output feedback stabilization control of a linear periodically time-varying system provided by an embodiment of this application; Figure 3 is the eigenvalue distribution diagram of an actual power system in a certain area provided by an embodiment of this application; Figure 4 is the schematic structural diagram of the device for output feedback stabilization control design of a linear periodically time-varying system provided by an embodiment of this application; Figure 5 is the schematic structural diagram of an electronic device provided by an embodiment of this application. Detailed Description of the Embodiments

[0020] In order to make the objectives, technical solutions, and advantages of this application clearer, the following further details this application in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not used to limit this application.

[0021] The term "and / or" in this text is an association relationship describing associated objects, indicating that three relationships can exist. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, and B exists alone. The symbol " / " in this text represents an "or" relationship between associated objects. For example, A / B represents A or B.

[0022] In the embodiments of the present application, words such as "exemplary" or "for example" are used to represent examples, illustrations, or explanations. Any embodiment or design solution described as "exemplary" or "for example" in the embodiments of the present application should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Rather, the use of words such as "exemplary" or "for example" is intended to present relevant concepts in a specific manner.

[0023] In the description of the embodiments of the present application, unless otherwise specified, the meaning of "a plurality of" refers to two or more. For example, a plurality of processing units refers to two or more processing units, etc.; a plurality of elements refers to two or more elements, etc.

[0024] First, the following content will be introduced: The theoretical basis for the dynamic stability analysis and stabilization control of existing linear periodically time-varying systems is the Floquet-Lyapunov theory. In this theory, the equation of the linear periodically time-varying system is:

[0025] Where, is the n -dimensional state variable, is the p -dimensional input variable, is the q -dimensional output variable, A ( t ), B ( t ) and C ( t ) are the n × n -dimensional system matrix, n × p -dimensional input matrix, and q × n -dimensional output matrix of the linear periodically time-varying system, respectively, and all satisfy: A ( t ) = A ( t + T ), B ( t ) = B ( t + T ), C ( t ) = C ( t + T ), where T is the minimum period of the system.

[0026] The general solution of the above linear periodically time-varying system can be expressed as:

[0027] Among them, Φ( t , 0) is the state transition matrix, is the initial value of the state variable.

[0028] The Floquet-Lyapunov theory states that ln(Φ( T , 0)) / T 's eigenvalues λ determine the dynamic stability of the linear periodically time-varying system. If there exists an eigenvalue λ with a real part greater than 0 for the linear periodically time-varying system, it indicates that this eigenvalue is negative damping and the linear periodically time-varying system is unstable; if there exists an eigenvalue λ with a real part less than 0 but close to the imaginary axis, it indicates that this eigenvalue is weak damping and the linear periodically time-varying system is stable but with a low stability margin; if all eigenvalues λ have a real part less than 0 and are far from the imaginary axis, it indicates that the linear periodically time-varying system is stable and has a high stability margin.

[0029] Next, in combination with Figures 1 - 3 the output feedback stabilization control design method for the linear periodically time-varying system provided in the embodiments of the present application will be introduced.

[0030] Figure 1 is one of the flow schematic diagrams of the output feedback stabilization control design method for the linear periodically time-varying system provided in the embodiments of the present application. As Figure 1 shown, the method includes the following steps: Step 100, based on the linear periodically time-varying system, obtain the state transition matrix through numerical calculation methods; Specifically, for the following equation:

[0031] Use numerical calculation methods to solve for the state transition matrix Φ( t at time t , 0) and the state transition matrix Φ( at time , 0), and then the state transition matrix Φ( t , ) = Φ( t , 0)Φ -1 ( , 0) can be solved.

[0032] Step 110, based on the state transition matrix and the preset new input variable, obtain the transformed input variable, the transformed output variable, and the discrete linear time-invariant system; Step 120, based on the discrete linear time-invariant system, the preset new input variable, and the transformed output variable, design an observer and a state feedback control law; Step 130: Based on the transformed input variables, transformed output variables, observer, state feedback control law, and preset new input variables, construct the output feedback stabilization control of the linear periodic time-varying system.

[0033] The output feedback stabilization control design method for the linear periodic time-varying system proposed by the present invention is generally applicable to scenarios such as electromagnetic oscillation suppression in power systems, spacecraft flight attitude control, and fan blade vibration suppression, ensuring the safe and stable operation of the above engineering practical scenarios.

[0034] A design method for output feedback stabilization control of a linear periodic time-varying system provided by this application constructs the output feedback stabilization control of the linear periodic time-varying system based on the transformed input variables, transformed output variables, observer, and preset new input variables. It can configure the closed-loop system eigenvalues to the desired positions, thereby increasing the damping of the negative-damping / weak-damping oscillation modes of the linear periodic time-varying system, effectively realizing system stabilization, and the solution does not require the introduction of strict mathematical conditions and assumptions, with a wider application range and can be applied to general linear periodic time-varying systems.

[0035] In some embodiments, the preset new input variable is calculated by the formula where is the preset new input variable in the th period, is a n × n dimensional matrix, is the observer state in the th period.

[0036] Optionally, the state feedback control law K is preset in advance.

[0037] In some embodiments, step 110 specifically includes: Construct the transformed input variable as where is the transformed input variable, is the transpose of the t × n input matrix of the linear periodic time-varying system at time p , is the state transition matrix, is the preset new input variable, is t / T the integer after rounding, T is the minimum period of the linear periodic time-varying system.

[0038] is the preset new input variable, in the time interval , ( + 1) T is constant within

[0039] In some embodiments, step 110 specifically includes: Construct the transformed output variable as , where is the transformed output variable of the th period, is the state transition matrix, is the transpose of the output matrix of the linear periodic time-varying system at time, is the output variable at is / T the integer after rounding down, T is the minimum period of the linear periodic time-varying system.

[0040] is the transformed output variable of the th period and is constant within the time interval , ( + 1) T .

[0041] In some embodiments, step 110 specifically includes: Based on the state transition matrix, obtain matrices W r ( T , 0), W o ( T , 0) and W c ( T , 0); Based on matrices W r ( T , 0), W o ( T , 0) and W c ( T , 0), construct a discrete linear time-invariant system , where , is the preset new input variable of the th period, is the sampled value of the state variable of the linear periodic time-varying system at time, is the transformed output variable of the th period, is the state transition matrix, is the identity matrix.

[0042] Specifically, first, based on the state transition matrix, calculate the matrix W r ( T , 0), W o ( T , 0) and W c ( T , 0) as follows:

[0043]

[0044]

[0045] Among them, , and are the state transition matrices, is the -moment n × p -dimensional input matrix, is the -moment q × n -dimensional output matrix, is the t -moment q × n -dimensional output matrix, and the superscript T represents the matrix transpose.

[0046] Then, based on the above matrices W r ( T , 0), W o ( T , 0) and W c ( T , 0), construct the following discrete linear time-invariant system:

[0047] Among them, .

[0048] Optionally, after constructing the discrete linear time-invariant system, a state feedback control law K can be designed for the discrete linear time-invariant system such that( A e – B e KThe eigenvalues of () are the desired eigenvalues .

[0049] In some embodiments, step 120 specifically includes: Design the observer as , where is n × n dimensional matrix, is the preset new input variable in the th cycle, is the transformed output variable in the th cycle, is the observer state in the +1 th cycle, is the observer state in the th cycle.

[0050] Optionally, is n × n dimensional matrix such that the absolute value of the real part of the eigenvalues of ( A e – LC e ) is 3 to 10 times the absolute value of the real part of the desired eigenvalue absolute value of the real part.

[0051] Figure 2 is the second flowchart of the output feedback stabilization control design method for a linear periodic time-varying system provided by the embodiments of the present application. As Figure 2 shown, in an embodiment of the present application, the steps of the method are as follows: S1. For the equation , use numerical calculation methods to solve the state transition matrix Φ( t , 0) at time t and the state transition matrix Φ( , 0) at time . Furthermore, the state transition matrix Φ( t , ) = Φ( t , 0)Φ -1 ( , 0) can be solved; S2. Calculate the matrices W r ( T , 0), W o ( T , 0) and W c ( T , 0) as follows:

[0052]

[0053]

[0054] S3. Construct the input transformation and output transformation:

[0055]

[0056] S4. Construct the following discrete linear time-invariant system:

[0057] S5. For the above discrete linear time-invariant system, design a state feedback control law K , such that the eigenvalues of ( A e – B e K ) are the desired eigenvalues, and determine the new input variable ; S6. For the above discrete linear time-invariant system, design L , such that the absolute value of the real part of the eigenvalues of ( A e – LC e ) is 3 to 10 times the absolute value of the real part of the desired eigenvalues, and construct an observer: ; S7. Synthesize the relationship:

[0058]

[0059]

[0060]

[0061] to form the output feedback stabilization control of the linear periodic time-varying system .

[0062] The eigenvalues of the closed-loop system after introducing the control are the eigenvalues of ( A e – B e K ) and the eigenvalues of ( A e – LC e) The eigenvalues. The real parts of the above matrix eigenvalues are all less than 0 and far from the imaginary axis. Therefore, the final closed-loop system has a high stability margin.

[0063] Figure 3 is the eigenvalue distribution diagram of an actual power system in a certain area provided by an embodiment of the present application. As Figure 3 shown, in an embodiment of the present application, the Floquet-Lyapunov theory is used to perform small-signal stability analysis on an actual power system in a certain area, and it is found that there are eigenvalues 0.43±j73.59 in the system, indicating that the system is unstable. By using the output feedback stabilization control design method for linear periodic time-varying systems provided by the present application, the unstable eigenvalues of the system are configured to be near –20±j70. At this time, all the eigenvalues of the system are located on the left side of the imaginary axis, indicating that the system is stable. This verifies the effectiveness of the output feedback stabilization control design method for linear periodic time-varying systems provided by the present application.

[0064] Figure 4 is the structural schematic diagram of the output feedback stabilization control design device for linear periodic time-varying systems provided by an embodiment of the present application. As Figure 4 shown, the system includes a first acquisition module 410, a second acquisition module 420, a design module 430, and a construction module 440, where: The first acquisition module 410 is used to obtain the state transition matrix based on the linear periodic time-varying system through a numerical calculation method; The second acquisition module 420 is used to obtain the transformed input variable, the transformed output variable, and the discrete linear time-invariant system based on the state transition matrix and a preset new input variable; The design module 430 is used to design an observer and a state feedback control law based on the discrete linear time-invariant system, the preset new input variable, and the transformed output variable; The construction module 440 is used to construct the output feedback stabilization control of the linear periodic time-varying system based on the transformed input variable, the transformed output variable, the observer, the state feedback control law, and the preset new input variable.

[0065] It should be understood that the above system is used to execute the method in the above embodiment. The corresponding program modules in the system have the same implementation principle and technical effects as those described in the above method. The working process of the system can refer to the corresponding process in the above method and will not be elaborated here.

[0066] Based on the method in the above embodiment, Figure 5 illustrates the entity structural schematic diagram of an electronic device. As Figure 5As shown in the figure, an embodiment of the present application provides an electronic device, which may include: a processor 510, a communications interface 520, a memory 530, and a communication bus 540. Among them, the processor 510, the communications interface 520, and the memory 530 complete communication with each other through the communication bus 540. The processor 510 may call the logical instructions in the memory 530 to execute the linear periodic time-varying system output feedback stabilization control design method in the above embodiment.

[0067] In addition, when the logical instructions in the above-mentioned memory 530 are implemented in the form of a software functional unit and sold or used as an independent product, they may be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, or a part of this technical solution, may be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the linear periodic time-varying system output feedback stabilization control design method described in each embodiment of the present application.

[0068] Based on the method in the above embodiment, an embodiment of the present application provides a computer-readable storage medium. The computer-readable storage medium stores a computer program. When the computer program runs on a processor, it causes the processor to execute the linear periodic time-varying system output feedback stabilization control design method in the above embodiment.

[0069] Based on the method in the above embodiment, an embodiment of the present application provides a computer program product. When the computer program product runs on a processor, it causes the processor to execute the linear periodic time-varying system output feedback stabilization control design method in the above embodiment.

[0070] It can be understood that the processor in the embodiment of the present application may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0071] The method steps in the embodiments of this application can be implemented in a hardware manner or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, and the software modules can be stored in a random access memory (RAM), flash memory, read-only memory (ROM), programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), registers, hard disks, removable hard disks, CD-ROMs, or any other form of storage medium well-known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can be located in an ASIC.

[0072] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the processes or functions described in the embodiments of this application are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center in a wired manner (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wirelessly (such as infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that the computer can access or a data storage device such as a server or data center that includes one or more integrated available media. The available medium can be a magnetic medium (such as a floppy disk, hard disk, magnetic tape), an optical medium (such as a DVD), or a semiconductor medium (such as a solid state disk (SSD)), etc.

[0073] It can be understood that the various numerical numbers involved in the embodiments of this application are only for convenience of description and are not used to limit the scope of the embodiments of this application.

[0074] Those skilled in the art can easily understand that the above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present application shall be included within the protection scope of the present application.

Claims

1. A design method for output feedback stabilization control of a linear periodic time-varying system, characterized in that, Including: Based on a linear periodic time-varying system, obtaining a state transition matrix through a numerical calculation method; Based on the state transition matrix and a preset new input variable, obtaining a transformed input variable, a transformed output variable, and a discrete linear time-invariant system; Based on the discrete linear time-invariant system, the preset new input variable, and the transformed output variable, designing an observer and a state feedback control law; Based on the transformed input variable, the transformed output variable, the observer, the state feedback control law, and the preset new input variable, constructing an output feedback stabilization control for the linear periodic time-varying system.

2. The output feedback stabilization control design method for the linear periodic time-varying system according to claim 1, characterized in that The preset new input variable is obtained through the formula where is the preset new input variable in the th cycle, is a n × n dimensional matrix, is the observer state in the th cycle.

3. The design method of output feedback stabilization control for a linear periodic time-varying system according to claim 1, characterized in that, The constructing the transformed input variable, the transformed output variable, and the discrete linear time-invariant system based on the state transition matrix and the preset new input variable includes: The input variable after the structural transformation is , where is the input variable after the transformation, is the transpose of the t -dimensional input matrix of the linear periodic time-varying system at time n × p , is the state transition matrix, is the preset new input variable, is t / T the integer after rounding, T is the minimum period of the linear periodic time-varying system.

4. The output feedback stabilization control design method for a linear periodic time-varying system according to claim 1, characterized in that, The constructing the transformed input variable, the transformed output variable, and the discrete linear time-invariant system based on the state transition matrix and the preset new input variable includes: The output variable after the structural transformation is , where is the output variable after transformation in the th cycle, is the state transition matrix, is the transpose of the output matrix of the linear periodic time-varying system at time, is the output variable at time, is / T the integer after rounding, T is the minimum period of the linear periodic time-varying system.

5. The design method for output feedback stabilization control of a linear periodic time-varying system according to claim 1, characterized in that, The constructing the transformed input variable, the transformed output variable, and the discrete linear time-invariant system based on the state transition matrix and the preset new input variable includes: Based on the state transition matrix, obtain the matrix W r ( T , 0), W o ( T , 0) and W c ( T , 0); Based on the said matrix W r ( T , 0), W o ( T , 0) and W c ( T , 0), a discrete linear time-invariant system is constructed, where , is the preset new input variable for the -th period, is the sampled value of the state variable of the linear periodic time-varying system at the -th moment, is the transformed output variable for the -th period, is the state transition matrix, is the identity matrix.

6. The design method for output feedback stabilization control of a linear periodic time-varying system according to claim 5, characterized in that The designing the observer based on the discrete linear time-invariant system includes: The designed observer is , where is n × n dimensional matrix, is the preset new input variable in the th cycle, is the transformed output variable in the th cycle, is the observer state in the +1 th cycle, is the observer state in the th cycle.

7. A device for designing output feedback stabilization control of a linear periodic time-varying system, characterized in that, Including: A first obtaining module, configured to obtain a state transition matrix based on a linear periodic time-varying system through a numerical calculation method; A second obtaining module, configured to obtain a transformed input variable, a transformed output variable, and a discrete linear time-invariant system based on the state transition matrix and a preset new input variable; A designing module, configured to design an observer and a state feedback control law based on the discrete linear time-invariant system, the preset new input variable, and the transformed output variable; A constructing module, configured to construct an output feedback stabilization control for the linear periodic time-varying system based on the transformed input variable, the transformed output variable, the observer, the state feedback control law, and the preset new input variable.

8. An electronic device, characterized in that, Including: At least one memory, configured to store a computer program; At least one processor, configured to execute the program stored in the memory. When the program stored in the memory is executed, the processor is configured to execute the method for designing an output feedback stabilization control for a linear periodic time-varying system according to any one of claims 1-6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program runs on the processor, the processor is caused to execute the method for designing an output feedback stabilization control for a linear periodic time-varying system according to any one of claims 1-6.

10. A computer program product, characterized in that, When the computer program product runs on the processor, the processor is caused to execute the method for designing an output feedback stabilization control for a linear periodic time-varying system according to any one of claims 1-6.

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