Controllable and observable quantitative analysis method and device for linear period time-varying system mode

Abstract

The invention belongs to the technical field of linear system dynamics analysis, and particularly discloses a controllable and observable quantitative analysis method and device for a linear period time-varying system mode. According to the method, the solution of the state variable of the system under multiple groups of initial values is solved through a numerical calculation method, so that the state transition matrix is obtained more accurately. The eigenvalue and the eigenvector of the state transition matrix correspond to the oscillation mode of the system, and the incidence relation between the input / output and the oscillation mode is established by solving the eigenvalue and the eigenvector. By calculating the mode controllability and the mode observability of the linear period time-varying system, the incidence relation between the input / output of the linear period time-varying system and the oscillation mode is accurately quantified, and a dynamic stability analysis theory system of the linear period time-varying system is further improved; the method is of great significance to stability mechanism analysis, stability rule description and the like of a large-scale linear periodic time-varying system, and theoretical support is provided for design and implementation of stabilization control of the linear periodic time-varying system.

Description

Technical Field

[0001] This application belongs to the technical field of linear system dynamics analysis, and more specifically, relates to a method and device for quantifying the controllability and observability of the modes of a linear periodically time-varying system. Background Art

[0002] In the real physical world, actual systems generally exhibit non-linear and time-varying characteristics. When analyzing the small-signal stability of an actual system, a linear periodically time-varying model is usually obtained based on the linearization of the system's steady-state trajectory. Linear periodically time-varying models are widespread in actual scenarios such as power systems, spacecraft, and celestial body motion. The theory of dynamic stability analysis for such models is of great significance for solving stability analysis and control problems in the above-mentioned engineering and physical scenarios.

[0003] The existing theory of dynamic stability analysis for linear periodically time-varying systems, with the Floquet-Lyapunov theory as the core, mainly analyzes whether a linear periodically time-varying system is stable, provides a theoretical basis for the stability criterion of linear periodically time-varying systems, and solves the problem of calculating the oscillation modes of linear periodically time-varying systems. However, for the description of the correlation mechanism between the input / output and oscillation modes of linear periodically time-varying systems, that is, the analysis of mode controllability and observability, the relevant theory is still incomplete. This also hinders the design and implementation of the stabilization control of linear periodically time-varying systems. Summary of the Invention

[0004] Aiming at the deficiencies of the existing technology, the purpose of this application is to provide a method and device for quantifying the controllability and observability of the modes of a linear periodically time-varying system, aiming to solve the problem that the incomplete relevant theory for describing the correlation mechanism between the input / output and oscillation modes of a linear periodically time-varying system in the existing technology hinders the design and implementation of the stabilization control of linear periodically time-varying systems.

[0005] To achieve the above purpose, in the first aspect, this application provides a method for quantifying the controllability and observability of the modes of a linear periodically time-varying system, including: Using numerical calculation methods to solve the dimensional state variables of the linear periodically time-varying system under groups of linearly independent initial value vectors; According to the solutions, determine the state transition matrix at time, and solve the eigenvalues and eigenvectors of the state transition matrix, being the minimum period of the linear periodically time-varying system; According to the eigenvalues and eigenvectors, determine the periodically time-varying matrix; According to the periodically time-varying matrix, determine the mode controllability and mode observability of the linear periodically time-varying system, and based on the mode controllability and mode observability, analyze the linear periodically time-varying system.

[0006] In some embodiments, determining a periodic time-varying matrix according to eigenvalues and eigenvectors includes: Solving a diagonal matrix formed by oscillation modes of a linear periodic time-varying system according to eigenvalues; Determining the periodic time-varying matrix according to the diagonal matrix, eigenvectors, and the system matrix of the linear periodic time-varying system.

[0007] In some embodiments, determining the mode observability of a linear periodic time-varying system according to the periodic time-varying matrix includes: Determining the mode observability according to the periodic time-varying matrix and the output matrix of the linear periodic time-varying system.

[0008] In some embodiments, determining the mode controllability of a linear periodic time-varying system according to the periodic time-varying matrix includes: Determining the mode controllability according to the periodic time-varying matrix and the input matrix of the linear periodic time-varying system.

[0009] In some embodiments, a set of linearly independent initial value vectors is determined according to any column in the n-dimensional identity matrix.

[0010] In some embodiments, the method further includes: Determining the relative magnitudes of the influences of different input variables of the linear periodic time-varying system on the concerned oscillation mode according to the mode controllability; Determining the relative magnitudes of the reflections of different output variables of the linear periodic time on the concerned oscillation mode according to the mode observability.

[0011] In a second aspect, the present application provides a device for quantitatively analyzing the mode controllability and observability of a linear periodic time-varying system, including: A first calculation module for solving, by using a numerical calculation method, the n-dimensional state variables of the linear periodic time-varying system under a set of linearly independent initial value vectors; A second calculation module for determining, according to the solution, the state transition matrix at time t, and solving the eigenvalues and eigenvectors of the state transition matrix, where T is the minimum period of the linear periodic time-varying system; A third calculation module for determining the periodic time-varying matrix according to the eigenvalues and eigenvectors; An analysis module for determining the mode controllability and mode observability of the linear periodic time-varying system according to the periodic time-varying matrix, and analyzing the linear periodic time-varying system based on the mode controllability and mode observability.

[0012] In a third aspect, the present application provides an electronic device, including: at least one memory for storing a program; and 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 method described in the first aspect or any of some embodiments of the first aspect.

[0013] 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, the processor is caused to execute the method described in the first aspect or any of some embodiments of the first aspect.

[0014] In a fifth aspect, the present application provides a computer program product, and when the computer program product runs on a processor, the processor is caused to execute the method described in the first aspect or any of some embodiments of the first aspect.

[0015] Generally speaking, compared with the prior art, the above technical solutions conceived by the present application have the following beneficial effects: The embodiment of the present application provides a method and device for quantitatively analyzing the controllability and observability of the modes of a linear periodically time-varying system. By using a numerical calculation method to solve the solutions of the state variables of the system under multiple sets of initial values, the state transition matrix can be obtained more accurately. The eigenvalues and eigenvectors of the state transition matrix correspond to the oscillation modes of the system. By solving the eigenvalues and eigenvectors, the correlation between the input / output and the oscillation modes is established. By calculating the mode controllability and mode observability of the linear periodically time-varying system, the correlation between the input / output and the oscillation modes of the linear periodically time-varying system is accurately quantified, further improving the dynamic stability analysis theoretical system of the linear periodically time-varying system, which is of great significance for the stability mechanism analysis and stability law characterization of large-scale linear periodically time-varying systems, and provides theoretical support for the design and implementation of the stabilization control of linear periodically time-varying systems. Description of the Drawings

[0016] Figure 1 is a schematic flow chart of the method for quantitatively analyzing the controllability and observability of the modes of a linear periodically time-varying system provided by the embodiment of the present application; Figure 2 is a schematic structural diagram of the device for quantitatively analyzing the controllability and observability of the modes of a linear periodically time-varying system provided by the embodiment of the present application; Figure 3 is a schematic structural diagram of the electronic device provided by the embodiment of the present application. Detailed Embodiments

[0017] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0018] As used herein, the term "and / or" describes the relationship between associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, and B exists alone. The symbol " / " herein represents an "or" relationship between associated objects. For example, A / B represents A or B.

[0019] In the embodiments of this application, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary" or "for example" in the embodiments of this application should not be construed as more preferred or more advantageous than other embodiments or designs. Rather, the use of words such as "exemplary" or "for example" is intended to present relevant concepts in a specific manner.

[0020] In the description of the embodiments of this application, unless otherwise specified, "a plurality of" means two or more.

[0021] In the related art, a linear periodically time-varying system can be expressed as:

[0022] where, is the dimensional state variable of the linear periodically time-varying system, is the derivative of, is the dimensional input variable of the linear periodically time-varying system, is the dimensional output variable of the linear periodically time-varying system, , and are respectively the dimensional system matrix, dimensional input matrix and dimensional output matrix of the linear periodically time-varying system, all of which have periodically time-varying characteristics, that is, , , , where, is the minimum period of the linear periodically time-varying system, represents conjugate transpose, is the time variable.

[0023] The mathematical form of the solution of the linear periodically time-varying system is:

[0024] where, is the state transition matrix, is the initial value of the state variable.

[0025] It can be further expressed as:

[0026] Wherein, is a p-dimensional periodic time-varying matrix, , and is also a q-dimensional periodic time-varying matrix, is the value of the periodic time-varying matrix at time 0; The p×q matrix is in the Jordan canonical form.

[0027] According to the Floquet-Lyapunov theory, the eigenvalues of the state transition matrix at time t determine the stability of the linear periodic time-varying system, while the diagonal elements of and are the oscillation modes of the linear periodic time-varying system. The periodic time-varying matrices

[0028] Wherein, is the derivative of is the derivative of

[0029] The above-mentioned Floquet-Lyapunov theory provides a stability criterion for linear periodic time-varying systems and solves the problem of calculating the oscillation modes of linear periodic time-varying systems. However, for the description of the correlation mechanism between the input / output and oscillation modes of linear periodic time-varying systems, that is, the analysis of mode controllability and observability, the relevant theory is still incomplete. This also hinders the design and implementation of the stabilization control of linear periodic time-varying systems. In the embodiments of the present application, the stabilization control refers to making the originally potentially unstable linear periodic time-varying system asymptotically stable by designing a controller.

[0030] Based on this, the embodiments of the present application provide a method and device for quantifying the controllability and observability of modes of a linear periodic time-varying system, the purpose of which is to quantify the influence degree of the input of the linear periodic time-varying system on the oscillation modes and the reflection degree of the output on the oscillation modes, and to describe the correlation characteristics between the input / output and modes of the linear periodic time-varying system, so as to determine the system input and output with strong correlation characteristics with the oscillation modes of concern, and provide theoretical support for the subsequent design and implementation of the stabilization control of linear periodic time-varying systems. The specific implementation is as follows.

[0031] The embodiments of the present application will be described below with reference to the accompanying drawings in the embodiments of the present application.

[0032] Please refer to Figure 1 , an embodiment of the present application provides a method for controllability and observability quantization analysis of a linear periodic time-varying system, including: Step 110 to Step 140.

[0033] In Step 110, a numerical calculation method is used to solve the -dimensional state variables of the linear periodic time-varying system under groups of linearly independent initial value vectors; In Step 120, according to the solution, the state transition matrix at is determined, and the eigenvalues and eigenvectors of the state transition matrix are solved. is the minimum period of the linear periodic time-varying system; In Step 130, according to the eigenvalues and eigenvectors, the periodic time-varying matrix is determined; In Step 140, according to the periodic time-varying matrix, the mode controllability and mode observability of the linear periodic time-varying system are determined, and based on the mode controllability and mode observability, the linear periodic time-varying system is analyzed.

[0034] In the embodiment of the present application, for the following linear periodic time-varying system:

[0035] Use a numerical calculation method to solve at groups of linearly independent initial value vectors under the solution.

[0036] Furthermore, in some embodiments, groups of linearly independent initial value vectors are determined according to any column in the

[0037] Specifically, groups of linearly independent initial value vectors can be taken as any column of the -dimensional identity matrix, and then calculate the solution of the linear periodic time-varying system within one period (for example ), denoted as: , and then there is a state transition matrix to respectively represent the -dimensional state variables of the linear periodic time-varying system under the first to the groups of linearly independent initial value vectors.

[0038] From the above state transition matrix , the state transition matrix at can be obtained, and calculated through the following formula Eigenvalues and eigenvectors:

[0039] Among them, among them, is the diagonal matrix composed of eigenvalues, and the eigenvectors include (right eigenvector) and (left eigenvector).

[0040] In the embodiments of the present application, is a single-period state transition matrix, and its eigenvalues and eigenvectors determine the long-term stability of the linear periodic time-varying system.

[0041] According to the diagonal matrix composed of the eigenvalues obtained above , the right eigenvector and the left eigenvector , calculate the periodic time-varying matrix.

[0042] According to the periodic time-varying matrix, calculate the mode controllability and mode observability of the linear periodic time-varying system, and use the mode controllability and the mode observability as the dynamic stability analysis indexes of the linear periodic time-varying system to perform dynamic stability analysis on the linear periodic time-varying system.

[0043] The embodiments of the present application provide a method for quantitatively analyzing the mode controllability and observability of a linear periodic time-varying system. By using a numerical calculation method to solve the solutions of the state variables of the system under multiple sets of initial values, the state transition matrix can be obtained more accurately. The eigenvalues and eigenvectors of the state transition matrix correspond to the oscillation modes of the system. By solving the eigenvalues and eigenvectors, the correlation relationship between the input / output and the oscillation modes is established. By calculating the mode controllability and mode observability of the linear periodic time-varying system, the correlation relationship between the input / output and the oscillation modes of the linear periodic time-varying system is accurately quantified, further improving the dynamic stability analysis theoretical system of the linear periodic time-varying system, which is of great significance for the stability mechanism analysis and stability law characterization of large-scale linear periodic time-varying systems, and provides theoretical support for the design and implementation of the stabilization control of the linear periodic time-varying system.

[0044] Furthermore, in some embodiments, determining the periodic time-varying matrix according to the eigenvalues and eigenvectors includes: According to the eigenvalues, solve the diagonal matrix composed of the oscillation modes of the linear periodic time-varying system; According to the diagonal matrix, the eigenvectors and the system matrix of the linear periodic time-varying system, determine the periodic time-varying matrix.

[0045] In the embodiments of the present application, substitute the diagonal matrix composed of the eigenvalues obtained above into the following formula to calculate the diagonal matrix composed of the oscillation modes of the linear periodic time-varying system :

[0046] Using the right eigenvector and the left eigenvector as the initial values, solve the following matrix differential equation:

[0047] where and are the periodically time-varying matrices obtained by solving.

[0048] Furthermore, in some embodiments, determining the mode controllability of a linear periodically time-varying system based on the periodically time-varying matrix includes: Determining the mode controllability based on the periodically time-varying matrix and the input matrix of the linear periodically time-varying system.

[0049] In the embodiments of the present application, the mode controllability of the th input for the th oscillation mode is calculated through the following expression :

[0050] where is the th row of the periodically time-varying matrix and is the th

[0051] Furthermore, in some embodiments, determining the mode observability of a linear periodically time-varying system based on the periodically time-varying matrix includes: Determining the mode observability based on the periodically time-varying matrix and the output matrix of the linear periodically time-varying system.

[0052] In the embodiments of the present application, the mode observability of the th input for the th oscillation mode is calculated through the following expression

[0053] where is the th column of the periodically time-varying matrix and is the Row.

[0054] Further, in some embodiments, the method further includes: Determine the relative magnitudes of the influences of different input variables of a linear periodically time-varying system on the oscillation mode of interest according to the mode controllability; Determine the relative magnitudes of the reflections of different output variables of a linear periodically time-varying system on the oscillation mode of interest according to the mode observability.

[0055] In the embodiments of the present application, the mode controllability of the linear periodically time-varying system obtained above can be used as the relative magnitude of the influence of different input variables of the linear periodically time-varying system on the oscillation mode of interest, and the mode observability of the linear periodically time-varying system obtained above can be used as the relative magnitude of the reflection of different output variables of the linear periodically time-varying system on the oscillation mode of interest.

[0056] The method for quantitatively analyzing the mode controllability and observability of a linear periodically time-varying system provided by the embodiments of the present application determines the inputs and outputs of the linear periodically time-varying system having strong correlation characteristics with the oscillation mode of interest by accurately quantifying the influence degree of the input of the linear periodically time-varying system on the oscillation mode and the reflection degree of the output on the oscillation mode, and further determines the selection of the inputs and outputs of the stabilizing controller, laying a foundation for the subsequent design and implementation of the stabilizing control of the linear periodically time-varying system.

[0057] Next, a device for quantitatively analyzing the mode controllability and observability of a linear periodically time-varying system provided by the present application will be described. The device for quantitatively analyzing the mode controllability and observability of a linear periodically time-varying system described below can be correspondingly referred to the method for quantitatively analyzing the mode controllability and observability of a linear periodically time-varying system described above.

[0058] Please further refer to Figure 2 , the embodiments of the present application provide a device for quantitatively analyzing the mode controllability and observability of a linear periodically time-varying system, including: a first calculation module 210, a second calculation module 220, a third calculation module 230, and an analysis module 240.

[0059] The first calculation module 210 is configured to solve the -dimensional state variables of the linear periodically time-varying system under groups of linearly independent initial value vectors by using a numerical calculation method; The second calculation module 220 is configured to determine, according to the solutions, the state transition matrix at the time, and solve the eigenvalues and eigenvectors of the state transition matrix, where An analysis module 240 is configured to determine the mode controllability and mode observability of a linear periodic time-varying system according to a periodic time-varying matrix, and analyze the linear periodic time-varying system based on the mode controllability and mode observability.

[0060] The linear periodic time-varying system mode controllability and observability quantization analysis device provided by the embodiments of the present application solves the solutions of the state variables of the system under multiple groups of initial values through a numerical calculation method to more accurately obtain the state transition matrix. The eigenvalues and eigenvectors of the state transition matrix correspond to the oscillation modes of the system. By solving the eigenvalues and eigenvectors, the correlation relationship between the input / output and the oscillation modes is established. By calculating the mode controllability and mode observability of the linear periodic time-varying system, the correlation relationship between the input / output and the oscillation modes of the linear periodic time-varying system is accurately quantified, further improving the dynamic stability analysis theoretical system of the linear periodic time-varying system, which is of great significance for the stability mechanism analysis and stability law characterization of large-scale linear periodic time-varying systems, and provides theoretical support for the design and implementation of the stabilization control of linear periodic time-varying systems.

[0061] It can be understood that the detailed function implementation of the above-mentioned each unit / module can refer to the introduction in the foregoing method embodiments, and will not be elaborated here.

[0062] It should be understood that the above-mentioned device is used to execute the method in the above-mentioned embodiments. The corresponding program modules in the device have the same implementation principle and technical effects as those described in the above method. The working process of the device can refer to the corresponding process in the above method, and will not be elaborated here.

[0063] Based on the method in the above-mentioned embodiments, the embodiments of the present application provide an electronic device. Please further refer to Figure 3 , the electronic device may include: a processor 310, a communications interface 320, a memory 330, and a communication bus 340. Among them, the processor 310, the communications interface 320, and the memory 330 communicate with each other through the communication bus 340. The processor 310 can call the logical instructions in the memory 330 to execute the method in the above-mentioned embodiments.

[0064] In addition, when the logical instructions in the above-mentioned memory 330 are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of this technical solution, can 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 methods described in various embodiments of this application.

[0065] Based on the method in the above-mentioned embodiment, an embodiment of this 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 method in the above-mentioned embodiment.

[0066] Based on the method in the above-mentioned embodiment, an embodiment of this application provides a computer program product. When the computer program product runs on a processor, it causes the processor to execute the method in the above-mentioned embodiment.

[0067] It can be understood that the processor in the embodiments of this application may be a central processing unit (CPU), or may also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field programmable gate arrays (FPGA), 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.

[0068] The method steps in the embodiments of the present 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, enabling the processor to 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.

[0069] 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 the present 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 a wireless manner (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.

[0070] It can be understood that the various numerical numbers involved in the embodiments of the present application are only for the convenience of description and do not limit the scope of the embodiments of the present application.

[0071] 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 method for controllable and observable quantization analysis of the mode of a linear periodic time-varying system, characterized in that, Including: Solving for the dimensional state variables of a linear periodically time-varying system under a set of linearly independent initial value vectors; Determine according to the solution the state transition matrix at the moment, and solve the eigenvalues and eigenvectors of the state transition matrix as the minimum period of the linear periodic time-varying system Determine a periodic time-varying matrix according to the eigenvalue and the eigenvector; Determine the mode controllability and mode observability of the linear periodic time-varying system according to the periodic time-varying matrix, and analyze the linear periodic time-varying system based on the mode controllability and the mode observability.

2. The method for quantifying the controllability and observability of the modes of a linear periodic time-varying system according to claim 1, wherein The determining the periodic time-varying matrix according to the eigenvalue and the eigenvector includes: Solve a diagonal matrix formed by the oscillation modes of the linear periodic time-varying system according to the eigenvalue; Determine the periodic time-varying matrix according to the diagonal matrix, the eigenvector and the system matrix of the linear periodic time-varying system.

3. The method for controllable and observable quantization analysis of the linear periodic time-varying system mode according to claim 1, wherein The determining the mode observability of the linear periodic time-varying system according to the periodic time-varying matrix includes: Determine the mode observability according to the periodic time-varying matrix and the output matrix of the linear periodic time-varying system.

4. The method for quantifiable analysis of controllability and observability of the modes of a linear periodic time-varying system according to claim 1, wherein The determining the mode controllability of the linear periodic time-varying system according to the periodic time-varying matrix includes: Determine the mode controllability according to the periodic time-varying matrix and the input matrix of the linear periodic time-varying system.

5. The method for controllable and observable quantization analysis of the linear periodic time-varying system mode according to claim 1, wherein The group of linearly independent initial value vectors is determined according to any column in the n-dimensional identity matrix.

6. The method for controllability and observability quantization analysis of a linear periodic time-varying system according to any one of claims 1-5, characterized in that, The method further includes: Determine the relative magnitudes of the influences of different input variables of the linear periodic time-varying system on the concerned oscillation mode according to the mode controllability; Determine the relative magnitudes of the reflections of different output variables of the linear periodic time on the concerned oscillation mode according to the mode observability.

7. A pattern controllable and observable quantization analysis device for a linear periodic time-varying system, characterized in that, Including: The first calculation module is used to solve the solutions of the -dimensional state variables of the linear periodic time-varying system under groups of linearly independent initial value vectors; A second calculation module, configured to determine, according to the solution, a state transition matrix at a moment, and solve eigenvalues and eigenvectors of the state transition matrix, as a minimum period of the linear periodic time-varying system; A third calculation module, configured to determine a periodic time-varying matrix according to the eigenvalue and the eigenvector; An analysis module, configured to determine the mode controllability and mode observability of the linear periodic time-varying system according to the periodic time-varying matrix, and analyze the linear periodic time-varying system based on the mode controllability and the mode observability.

8. An electronic device, characterized in that, Including: At least one memory for storing a computer 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 method 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 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 according to any one of claims 1-6.

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