H∞ control method for two-dimensional switched continuous discrete-time systems based on state dependence

Abstract

The present invention discloses a state-dependent H∞ control method for a two-dimensional switching continuous discrete system, comprising the following steps: obtaining a two-dimensional switching continuous discrete system model; constructing a state-dependent switching law that depends only on continuous variables to obtain a stability condition for the two-dimensional switching continuous discrete system; applying the stability condition for the two-dimensional switching continuous discrete system to a switching repetitive process to determine an along-channel stability condition for the two-dimensional switching continuous discrete system; and designing a state feedback control law that considers H∞ control of the switching repetitive process, so that the two-dimensional switching continuous discrete system has the desired H∞ performance. The method of the present invention relies only on the state-dependent switching law of continuous variables to analyze the stability of the two-dimensional switching continuous discrete system, obtains the stability condition using the Lyapunov function method, applies the stability result to the switching repetitive process, and implements H∞ control of the switching repetitive process by establishing a new state-dependent switching law.

Description

Technical Field

[0001] The present invention belongs to the field of multidimensional system and control technology, and in particular relates to an H∞ control method for a two-dimensional switching continuous discrete system based on state dependence. Background Art

[0002] Stability analysis and control of two-dimensional switched continuous discrete systems present complex technical challenges. These systems contain state components in both horizontal and vertical dimensions, and exhibit state-dependent switching behaviors, making the system dynamics extremely complex.

[0003] Traditional single-dimensional system analysis methods are difficult to directly apply, while existing multidimensional system theories cannot effectively handle switching behavior. Accurately characterizing the impact of state-dependent switching on system stability while accounting for the two-dimensional nature of the system has become a key issue that needs to be addressed. Furthermore, for the unique two-dimensional nature of switching repetitive processes, designing effective control strategies to ensure the closed-loop system's H∞ performance and along-channel stability is also a challenging problem.

[0004] Solving these problems requires not only the development of new theoretical analysis tools but also the consideration of various constraints in practical applications. Finding a balance between theoretical analysis and engineering practice to construct a systematic and effective method for stability analysis and control of two-dimensional switching systems is a major technical challenge facing research in this field. Summary of the Invention

[0005] The present invention aims to solve one of the technical problems existing in the related art at least to a certain extent.

[0006] One object of the present invention is to provide an H∞ control method for a two-dimensional switching continuous discrete system based on state dependence, which only relies on the state-dependent switching law of continuous variables to analyze the stability of the two-dimensional switching continuous discrete system, uses the Lyapunov function method to obtain the stability condition, applies the stability result to the switching repetitive process, and realizes H∞ control of the switching repetitive process by establishing a new state-dependent switching law.

[0007] In order to achieve the above-mentioned object, the present invention provides, on one hand, a state-dependent H∞ control method for a two-dimensional switching continuous discrete system, comprising:

[0008] S1. Obtain a two-dimensional switching continuous discrete system model;

[0009] S2. Construct a state-dependent switching law that depends only on continuous variables. Based on the stability condition of a two-dimensional continuous discrete system, extend it to a two-dimensional switched continuous discrete system and obtain the stability condition of a two-dimensional switched continuous discrete system.

[0010] S3, applying the stability condition of the two-dimensional switching continuous discrete system to the switching repetitive process to determine the along-channel stability condition of the two-dimensional switching continuous discrete system;

[0011] S4. Design a state feedback control law, consider H∞ control of the switching repetitive process, and make the two-dimensional switching continuous discrete system have the expected H∞ performance.

[0012] A further preferred technical solution of the present invention is that obtaining a two-dimensional switching continuous discrete system model in step S1 includes:

[0013] Determine the horizontal and vertical state components of the system;

[0014] Acquire a switching signal, and use the switching signal to indicate an activated subsystem;

[0015] According to the horizontal state component, the vertical state component and the switching signal, a two-dimensional switching continuous discrete system model including multiple subsystems is constructed, wherein the subsystems are represented by real number block matrices of appropriate dimension; the two-dimensional switching continuous discrete system model is expressed as:

[0016] ;

[0017] in is the horizontal component, , is the vertical component, is the control input, represents the channel length, is the number of channels; is the horizontal component The first derivative of ; is the system matrix, is the input matrix; Represents the switching signal, L is the number of subsystems, when Indicates the The subsystem is activated. , ,matrix is a real block matrix of appropriate dimension, is the appropriate-dimensional matrix; .

[0018] As a preference, the state-dependent switching law designed in step S2 is ,in ;

[0019] Choose the Lyapunov function, expressed as:

[0020] ;

[0021] in , is the dimensionally appropriate matrix;

[0022] The sufficient condition for determining the asymptotic stability of a two-dimensional switched continuous discrete system is:

[0023] (1) The boundary conditions of the system are smooth and bounded;

[0024] (2) and For all All are Hurwitz stable;

[0025] (3) If there exists a positive definite symmetric matrix and , and the Metzler matrix , so that the system switches

[0026] The following are satisfied:

[0027] ;

[0028] The Metzler matrix has non-negative off-diagonal elements and satisfies the constraints ;

[0029] After calculation under the above conditions , that is, the system is asymptotically stable.

[0030] Preferably, step S3 includes:

[0031] The switching repetitive process is regarded as a special switching 2-D continuous discrete system. Consider the following switching repetitive process:

[0032] ;

[0033] in is the channel length, is the number of channels, is the state variable, is the channel profile vector, is the input variable, is the expected output variable, is a bounded external disturbance; 、 、 、 、 、 、 、 、 and are all suitable-dimensional matrices, when Indicates the The subsystem is activated. , , , , , , , , , ;

[0034] When external disturbance When the switching repetitive process is in the state-dependent switching law The sufficient condition for the stability of the lower channel is:

[0035] There exists a positive definite symmetric matrix and , and the Metzler matrix , so that the system satisfies the inequality:

[0036] ;

[0037] in .

[0038] Preferably, step S4 specifically includes:

[0039] For a switching repetitive process, design a state feedback controller:

[0040] ;

[0041] in is the controller gain;

[0042] Substituting the switching repetitive process into the closed-loop system equation:

[0043] ;

[0044] in, is the closed-loop system matrix, ; is the input matrix for the closed-loop system, ; is the closed-loop system output matrix, ; is the closed-loop system transfer matrix, ; is the expected output matrix, ; is the expected transfer matrix, ;

[0045] The designed closed-loop system is stable along the channel under a given H∞ performance index γ if the closed-loop system satisfies the following conditions:

[0046] (1) When external disturbance When , the system is stable along the channel;

[0047] (2) Under the zero boundary condition, satisfy ;

[0048] in , ;

[0049] Design state-dependent switching law , calculate the state feedback controller The value of

[0050] For a given H∞ performance index γ, if there exists a positive definite symmetric matrix and , and the Metzler matrix π, so that the system satisfies the inequality:

[0051] ;

[0052] The system switches The lower edge channel is stable and meets the given H∞ performance index γ;

[0053] in , , , , , is the identity matrix;

[0054] And the following performance indicator function is given:

[0055] ;

[0056] ;

[0057] in ;

[0058] When external disturbance When the switching repetition process is determined by step S3 to be stable along the channel; Available ,but

[0059]

[0060] Under the initial condition of 0, , by the matrix and The positivity of and ,but , that is, the closed-loop system is stable along the channel and satisfies the given H∞ performance index ;

[0061] according to , after matrix operation, we get

[0062] ;

[0063] in , , , ;

[0064] , , , ; 、 All are dimensionally appropriate matrices;

[0065] The state feedback controller is obtained according to the LMI calculation method .

[0066] Another aspect of the present invention provides a non-transitory computer-readable storage medium having computer instructions stored thereon, which enable a computer to execute the above-mentioned state-dependent two-dimensional switching continuous discrete system H∞ control method.

[0067] Another aspect of the present invention provides an electronic device, comprising: a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other through the communication bus, and the processor calls the logic instructions in the memory to execute the above-mentioned state-dependent two-dimensional switching continuous discrete system H∞ control method.

[0068] On the other hand, the present invention provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer executes the above-mentioned state-dependent two-dimensional switching continuous discrete system H∞ control method.

[0069] Beneficial effects: The H∞ control method for a two-dimensional switching continuous discrete system based on state dependence of the present invention first establishes a 2-D switching system model containing horizontal and vertical state components, and constructs a state switching law that depends on continuous variables. Then, the sufficient conditions for the asymptotic stability of the system are derived using the Lyapunov function method, and are applied to the switching repetitive process. For the switching repetitive process, the present invention designs a state feedback control law, constructs a closed-loop system, and analyzes its H∞ performance and along-channel stability. The linear matrix inequality method is used to calculate the controller gain to achieve effective control of the system. Through simulation verification, the present invention can ensure the stability of the 2-D switching system under state-dependent switching, and has good H∞ disturbance suppression performance, providing a new theoretical method for the analysis and control of complex switching systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 This is a flow chart of the H∞ control method for a two-dimensional switching continuous discrete system based on state dependence of the present invention;

[0071] Figure 2 Schematic diagram of the metal rolling process in the verification example of the present invention;

[0072] Figure 3 is the process of change of system state variables in the example;

[0073] Figure 4 is the switching law designed in the example. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the embodiments described are part of the embodiments of the present invention, not all of the embodiments, and they should not be understood as limitations on the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. In the description of the present invention, it should be understood that the terms used are only for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0075] The following combination Figures 1-4 The present invention describes a state-dependent H∞ control method for a two-dimensional switching continuous discrete system.

[0076] Example 1: This example provides a two-dimensional switching continuous discrete system H∞ control method based on state dependence, such as Figure 1 Shown, including:

[0077] S1. Obtain a two-dimensional switching continuous discrete system model, which includes a horizontal state component and a vertical state component, as well as a switching signal that depends on the continuous variable t, and determine the number of subsystems and the corresponding real number block matrix. Specifically, it includes:

[0078] Determine the horizontal and vertical state components of the system;

[0079] Acquire a switching signal, and use the switching signal to indicate an activated subsystem;

[0080] According to the horizontal state component, the vertical state component and the switching signal, a two-dimensional switching continuous discrete system model including multiple subsystems is constructed, wherein the subsystems are represented by real number block matrices of appropriate dimension; the two-dimensional switching continuous discrete system model is expressed as:

[0081] ;

[0082] in is the horizontal component, , is the vertical component, is the control input, represents the channel length, is the number of channels; is the horizontal component The first derivative of ; is the system matrix, is the input matrix; Represents the switching signal, L is the number of subsystems, when Indicates the The subsystem is activated. , ,matrix is a real block matrix of appropriate dimension, is the appropriate-dimensional matrix; .

[0083] S2. Construct a state-dependent switching law that depends only on continuous variables. Based on the stability conditions of two-dimensional continuous discrete systems, generalize it to two-dimensional switching continuous discrete systems and obtain the stability conditions of two-dimensional switching continuous discrete systems. Specifically, it includes:

[0084] First, in the absence of switching, according to the existing conclusions, the sufficient condition for the asymptotic stability of a 2-D continuous discrete system is:

[0085] (1) The boundary conditions of the system are smooth and bounded;

[0086] (2) and It is Hurwitz stable;

[0087] (3) If there exists a positive definite symmetric matrix and , so that:

[0088] ;

[0089] in is the system matrix without switching.

[0090] For a two-dimensional switched continuous discrete system, the designed state-dependent switching law is ,in ;

[0091] Choose the Lyapunov function, expressed as:

[0092] ;

[0093] in , is the dimensionally appropriate matrix;

[0094] The sufficient condition for determining the asymptotic stability of a two-dimensional switched continuous discrete system is:

[0095] (1) The boundary conditions of the system are smooth and bounded;

[0096] (2) and For all All are Hurwitz stable;

[0097] (3) If there exists a positive definite symmetric matrix and , and the Metzler matrix , so that the system switches

[0098] The following are satisfied:

[0099] ;

[0100] The Metzler matrix has non-negative off-diagonal elements and satisfies the constraints ;

[0101] After calculation under the above conditions , that is, the system is asymptotically stable.

[0102] S3, applying the stability condition of the two-dimensional switching continuous discrete system to the switching repetitive process to determine the along-channel stability condition of the two-dimensional switching continuous discrete system. Specifically including:

[0103] The switching repetitive process is regarded as a special switching 2-D continuous discrete system. Consider the following switching repetitive process:

[0104] ;

[0105] in is the channel length, is the number of channels, is the state variable, is the channel profile vector, is the input variable, is the expected output variable, is a bounded external disturbance; 、 、 、 、 、 、 、 、 and are all suitable-dimensional matrices, when Indicates the The subsystem is activated. , , , , , , , , , ;

[0106] For a non-switching linear repetitive process, there are two concepts of stability: asymptotic stability and stability along the channel. The condition for asymptotic stability is the matrix The spectral radius is less than 1. At this time, the state performance of the system along the channel cannot be guaranteed. Therefore, it is necessary to further give the stability along the channel to describe the system performance. According to the existing conclusions, the stability condition of the linear repetitive process along the channel is: (1) Matrix The spectral radius is less than 1, (2) the matrix The eigenvalues ​​of have negative real parts, (3) ,in These conditions are equivalent to the conditions for asymptotic stability of 2-D continuous discrete systems, so the stability conditions in step S2 can be applied directly:

[0107] When external disturbance When the switching repetitive process is in the state-dependent switching law The sufficient condition for the stability of the lower channel is:

[0108] There exists a positive definite symmetric matrix and , and the Metzler matrix , so that the system satisfies the inequality:

[0109] ;

[0110] in .

[0111] S4. Design a state feedback control law, taking into account the H∞ control of the switching repetitive process, so that the two-dimensional switching continuous discrete system has the expected H∞ performance. Specifically including:

[0112] For a switching repetitive process, design a state feedback controller:

[0113] ;

[0114] in is the controller gain;

[0115] Substituting the switching repetitive process into the closed-loop system equation:

[0116] ;

[0117] in, is the closed-loop system matrix, ; is the input matrix for the closed-loop system, ; is the closed-loop system output matrix, ; is the closed-loop system transfer matrix, ; is the expected output matrix, ; is the expected transfer matrix, ;

[0118] The designed closed-loop system is stable along the channel under a given H∞ performance index γ if the closed-loop system satisfies the following conditions:

[0119] (1) When external disturbance When , the system is stable along the channel;

[0120] (2) Under the zero boundary condition, satisfy ;

[0121] in , ;

[0122] Design state-dependent switching law , calculate the state feedback controller The value of

[0123] For a given H∞ performance index γ, if there exists a positive definite symmetric matrix and , and the Metzler matrix π, so that the system satisfies the inequality:

[0124] ;

[0125] The system switches The lower edge channel is stable and meets the given H∞ performance index γ;

[0126] in , , , , , is the identity matrix;

[0127] And the following performance indicator function is given:

[0128] ;

[0129] ;

[0130] in ;

[0131] When external disturbance When the switching repetition process is determined by step S3 to be stable along the channel; Available ,but

[0132]

[0133] Under the initial condition of 0, , by the matrix and The positivity of and ,but , that is, the closed-loop system is stable along the channel and satisfies the given H∞ performance index ;

[0134] according to , after matrix operation, we get

[0135] ;

[0136] in , , , ;

[0137] , , , ; 、 All are dimensionally appropriate matrices;

[0138] The state feedback controller is obtained according to the LMI calculation method .

[0139] The method of this embodiment is described below through a specific example of a metal rolling process.

[0140] Consider Figure 2 The differential equation for the metal rolling process shown in Figure 1 can be expressed as:

[0141] ;

[0142] in For external force, is the quality of the roller gap adjustment mechanism, Under external force The displacement, To adjust the stiffness of the mechanism spring, is the hardness of the metal strip, .

[0143] By transformation, we can get the switching repetitive process and obtain the closed-loop system equation:

[0144] ;

[0145] Select the following values: 、 、 、 、 、 、 、 、 、 ;

[0146] 、 、 、 、 、 、 、 、 、 .

[0147] Initial state:

[0148] ;

[0149] ;

[0150] make , according to the conditions in step S4, LMI can be obtained, , , and an optimal performance index can be obtained .

[0151] Figure 3 It shows the changing trend of the system state. It can be seen that under the action of the switching law, by designing the state feedback controller, the final state and Both tend to 0, indicating that the system is stable along the channel and satisfies Performance indicators. Figure 4 The switching of the system between the two subsystems is given.

[0152] Embodiment 2: This embodiment provides a non-transitory computer-readable storage medium having computer instructions stored thereon. The computer instructions cause a computer to execute a state-dependent two-dimensional switched continuous discrete system H∞ control method, the method comprising the following steps:

[0153] S1. Obtain a two-dimensional switching continuous discrete system model;

[0154] S2. Construct a state-dependent switching law that depends only on continuous variables. Based on the stability condition of a two-dimensional continuous discrete system, extend it to a two-dimensional switched continuous discrete system and obtain the stability condition of a two-dimensional switched continuous discrete system.

[0155] S3, applying the stability condition of the two-dimensional switching continuous discrete system to the switching repetitive process to determine the along-channel stability condition of the two-dimensional switching continuous discrete system;

[0156] S4. Design a state feedback control law, consider H∞ control of the switching repetitive process, and make the two-dimensional switching continuous discrete system have the expected H∞ performance.

[0157] Embodiment 3: This embodiment provides an electronic device, which may include: a processor, a communications interface, a memory, and a communications bus, wherein the processor, the communications interface, and the memory communicate with each other via the communications bus. The processor may call logic instructions in the memory to execute a state-dependent two-dimensional switching continuous discrete system H∞ control method, which includes the following steps:

[0158] S1. Obtain a two-dimensional switching continuous discrete system model;

[0159] S2. Construct a state-dependent switching law that depends only on continuous variables. Based on the stability condition of a two-dimensional continuous discrete system, extend it to a two-dimensional switched continuous discrete system and obtain the stability condition of a two-dimensional switched continuous discrete system.

[0160] S3, applying the stability condition of the two-dimensional switching continuous discrete system to the switching repetitive process to determine the along-channel stability condition of the two-dimensional switching continuous discrete system;

[0161] S4. Design a state feedback control law, consider H∞ control of the switching repetitive process, and make the two-dimensional switching continuous discrete system have the expected H∞ performance.

[0162] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or a portion of the 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 enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage media include various media capable of storing program code, such as USB flash drives, mobile hard drives, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical disks.

[0163] Embodiment 4: This embodiment provides a computer program product, which includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can perform a state-dependent two-dimensional switched continuous discrete system H∞ control method, which includes the following steps:

[0164] S1. Obtain a two-dimensional switching continuous discrete system model;

[0165] S2. Construct a state-dependent switching law that depends only on continuous variables. Based on the stability condition of a two-dimensional continuous discrete system, extend it to a two-dimensional switched continuous discrete system and obtain the stability condition of a two-dimensional switched continuous discrete system.

[0166] S3, applying the stability condition of the two-dimensional switching continuous discrete system to the switching repetitive process to determine the along-channel stability condition of the two-dimensional switching continuous discrete system;

[0167] S4. Design a state feedback control law, consider H∞ control of the switching repetitive process, and make the two-dimensional switching continuous discrete system have the expected H∞ performance.

[0168] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0169] Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented using software plus a necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the essence of the above technical solution, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, or an optical disk, and includes a number of instructions for causing a computer device (such as a personal computer, server, or network device) to execute the methods described in each embodiment or certain portions of the embodiments.

[0170] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A state-dependent H∞ control method for two-dimensional switching continuous discrete systems, characterized in that: include: S1. Obtain a two-dimensional switching continuous discrete system model; including: Determine the horizontal and vertical state components of the system; Acquire a switching signal, and use the switching signal to indicate an activated subsystem; According to the horizontal state component, the vertical state component and the switching signal, a two-dimensional switching continuous discrete system model including multiple subsystems is constructed, wherein the subsystems are represented by real number block matrices of appropriate dimension; the two-dimensional switching continuous discrete system model is expressed as: ； in is the horizontal component, , is the vertical component, is the control input, represents the channel length, is the number of channels; is the horizontal component The first derivative of ; is the system matrix, is the input matrix; Represents the switching signal, L is the number of subsystems, when Indicates the The subsystem is activated. , ,matrix is a real block matrix of appropriate dimension, is the appropriate-dimensional matrix; ; S2. Construct a state-dependent switching law that depends only on continuous variables. Based on the stability condition of a two-dimensional continuous discrete system, it is extended to a two-dimensional switching continuous discrete system, and the stability condition of a two-dimensional switching continuous discrete system is obtained. The designed state-dependent switching law is: ,in ; Choose the Lyapunov function, expressed as: ； in , is a dimensionally appropriate matrix; The sufficient condition for determining the asymptotic stability of a two-dimensional switched continuous discrete system is: (1) The boundary conditions of the system are smooth and bounded; (2) and For all All are Hurwitz stable; (3) If there exists a positive definite symmetric matrix and , and the Metzler matrix , so that the system switches The following are satisfied: ； The Metzler matrix has non-negative off-diagonal elements and satisfies the constraints ; After calculation under the above conditions , that is, the system is asymptotically stable; S3, applying the stability condition of the two-dimensional switching continuous discrete system to the switching repetitive process to determine the along-channel stability condition of the two-dimensional switching continuous discrete system; comprising: The switching repetitive process is regarded as a special switching 2-D continuous discrete system. Consider the following switching repetitive process: ； in is the channel length, is the number of channels, is the state variable, is the channel profile vector, is the input variable, is the expected output variable, is a bounded external disturbance; 、 、 、 、 、 、 、 、 and are all suitable-dimensional matrices, when Indicates the The subsystem is activated. , , , , , , , , , ; When external disturbance When the switching repetitive process is in the state-dependent switching law The sufficient condition for the stability of the lower channel is: There exists a positive definite symmetric matrix and , and the Metzler matrix , so that the system satisfies the inequality: ； in ; S4. Designing a state feedback control law, taking into account H∞ control of the switching repetitive process, so that the two-dimensional switching continuous discrete system has the expected H∞ performance; specifically including: For a switching repetitive process, design a state feedback controller: ； in is the controller gain; Substituting the switching repetitive process into the closed-loop system equation: ； in, is the closed-loop system matrix, ; is the input matrix for the closed-loop system, ; is the closed-loop system output matrix, ; is the closed-loop system transfer matrix, ; is the expected output matrix, ; is the expected transfer matrix, ; The designed closed-loop system is stable along the channel under a given H∞ performance index γ if the closed-loop system satisfies the following conditions: (1) When external disturbance When , the system is stable along the channel; (2) Under the zero boundary condition, satisfy ; in , ; Design state-dependent switching law , calculate the state feedback controller The value of For a given H∞ performance index γ, if there exists a positive definite symmetric matrix and , and the Metzler matrix π, so that the system satisfies the inequality: ； The system switches The lower edge channel is stable and meets the given H∞ performance index γ; in , , , , , is the identity matrix; And the following performance indicator function is given: ； ； in ; When external disturbance When the switching repetition process is determined by step S3 to be stable along the channel; Available ,but ； Under the initial condition of 0, , by the matrix and The positivity of and ,but , that is, the closed-loop system is stable along the channel and satisfies the given H∞ performance index ; according to , after matrix operation, we get ； in , , , ; , , , ; 、 All are dimensionally appropriate matrices; The state feedback controller is obtained according to the LMI calculation method .

2. A non-transitory computer-readable storage medium, characterized in that Computer instructions are stored thereon, and the computer instructions enable the computer to execute the state-dependent two-dimensional switching continuous discrete system H∞ control method according to claim 1.

3. An electronic device, characterized in that: include: A processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other via the communication bus, and the processor calls logic instructions in the memory to execute the state-dependent two-dimensional switching continuous discrete system H∞ control method according to claim 1.

4. A computer program product, characterized in that The computer program product includes a computer program stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer executes the state-dependent two-dimensional switching continuous discrete system H∞ control method according to claim 1.

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