A robust control method and system for a multi-equilibrium point variable mode system

Abstract

The present invention provides a robust control method and system for a multi-equilibrium point variable modal system, which belongs to the field of control of hybrid systems. ∞ The controller is difficult to use for multi-equilibrium point variable modal systems, which limits the robustness of multi-equilibrium point variable modal systems in practical applications and has weak resistance to external interference. This paper considers the general situation of subsystems with different equilibrium points and proposes a stability and convergence region estimation method for multi-equilibrium point variable modal systems, thereby achieving more accurate control of the behavior of complex variable modal systems; and in response to the external interference problem that is prevalent in practical applications, an H ∞ The controller significantly enhances the variable modal system's resistance to external adverse interference, ensuring the system's stability and reliability. This innovation not only provides a new perspective for the study of variable modal systems, but also provides strong technical support for practical applications in related fields.

Description

Technical Field

[0001] The present invention relates to the technical field of control of hybrid systems, and in particular to a robust control method and system for a multi-equilibrium point variable mode system. Background Art

[0002] Modal systems are a special type of hybrid control system, consisting of multiple subsystems (modes) and modal signals. Modal system theory plays an important role in the modeling and control of physical systems with modal variation. It has been widely applied in fields such as unmanned aerial vehicle (UAV) flight control, robotic arm control, multi-agent system control, traffic management control, and chemical process control. In this context, in-depth research on control methods and robust control techniques for modal systems is crucial for ensuring the stability of control systems and improving their anti-interference capabilities.

[0003] In the field of variable modal systems research, system stability analysis and controller design are hot topics. Existing studies have mostly focused on the case where all subsystems have a common equilibrium point. In practical engineering applications such as power control, legged robots, and flapping-wing robots, each subsystem often has a different equilibrium point. Multi-equilibrium-point variable modal systems are an extension of conventional common-equilibrium-point variable modal systems and a more generalized control system model. The presence of multiple equilibrium points makes system behavior more complex. Existing control methods for variable modal systems are no longer applicable. When discussing the stability of multi-equilibrium-point variable modal systems, it is unrealistic to assume that the trajectory converges to a single point; rather, convergence to a specific region is more reasonable. Although a few studies have explored the stability conditions for multi-equilibrium-point variable modal systems, no clear controller design method has been proposed. A stability analysis method and controller design suitable for multi-equilibrium-point variable modal systems are urgently needed.

[0004] The L2 gain of a variable modal system is a key indicator for evaluating its control performance. The L2 gain can quantify the anti-interference ability of the control system. In modern industrial control, aerospace, and autonomous driving, the L2 gain performance directly affects the safety and reliability of the entire system. In the past few decades, a large number of studies have been devoted to the L2 gain analysis of common equilibrium point variable modal systems and have achieved remarkable results. These studies proposed the bounded real lemma and designed the H ∞ Controllers provide effective solutions for the stability and robust control of variable modal systems. However, these research results are also limited by the assumption of a common equilibrium point and are difficult to apply to multi-equilibrium variable modal systems. ∞ The research on controller design is still insufficient, which limits the improvement of robust performance of multi-equilibrium variable modal systems in practical applications. Therefore, the bounded real lemma of multi-equilibrium variable modal systems is studied, and a multi-equilibrium H∞ Variable mode controller has important theoretical value and practical significance in promoting the development of variable mode system control theory. Summary of the Invention

[0005] The technical problems to be solved by the present invention are:

[0006] In order to solve the problem that the existing H∞ controller is difficult to use in multi-equilibrium point variable modal systems, which limits the improvement of the robust performance of multi-equilibrium point variable modal systems in practical applications and has weak resistance to external disturbances.

[0007] The present invention is to solve the above technical problems using the following technical solutions:

[0008] The present invention provides a robust control method for a multi-equilibrium point variable mode system, comprising the following steps:

[0009] S100, establishing a control system model for a multi-equilibrium-point variable modal system, describing the multi-equilibrium-point variable modal system as a multi-equilibrium-point variable modal system with multiple equilibrium points and external disturbances, and then expanding the existing definitions of stability and L2 gain for the variable modal system;

[0010] S200. Based on the multi-Lyapunov function method, a Lyapunov function about the center of the convergence region is assigned to each mode with different equilibrium points. According to the rate of change of the Lyapunov function, a criterion for global consistent asymptotic regional stability is given. The stability of the multi-equilibrium variable mode system under the condition of average residence time is evaluated by this criterion.

[0011] S300. Based on the influence of variable mode and multi-equilibrium point characteristics on the L,gain performance index of the multi-equilibrium point variable mode system, an L,gain analysis method of the multi-equilibrium point variable mode system is established, and then a bounded real lemma in the form of linear matrix inequality is proposed;

[0012] S400 , designing an H∞ variable modal controller with mode-dependent state feedback for a multi-equilibrium variable modal system according to the bounded real lemma in the form of a linear matrix inequality proposed in step S300 .

[0013] Furthermore, in step S100, it specifically includes:

[0014] S110, the multi-equilibrium point variable modal system model is:

[0015]

[0016] in, is the state vector; is the control input vector; is the measurement output vector; w is the disturbance input vector belonging to L2[0,∞); σ(t)=i is the variable mode signal, indicating that mode i is currently activated; A is the state matrix; B is the input matrix; C is the output matrix; D is the direct transfer matrix; E is the disturbance input matrix; F is the disturbance output matrix;

[0017] and represent the equilibrium state, balanced input, and balanced output of mode i respectively;

[0018] S120. The stability of the expanded multi-equilibrium variable modal system is defined as:

[0019] For a multi-equilibrium variable modal system If there exists a positive constant δ and a KL-like function β such that for all variable modal signals σ, the solution of the system satisfies Then the multi-equilibrium point variable mode system is globally consistent and asymptotically stable:

[0020]

[0021] in,

[0022]

[0023] n represents the dimension of the state vector x; and R are Ω e The center and radius of

[0024] S130. The L2 gain of the expanded multi-equilibrium point variable modal system is defined as:

[0025] For a multi-equilibrium variable mode system, if the initial condition is x(t0), for If the following inequality holds, then the multi-equilibrium variable mode system has an unweighted L2 gain γ:

[0026]

[0027] in, It represents the deviation between the measured output and the current balanced output; C is a positive constant related to x(t0).

[0028] Furthermore, in step S200, it specifically includes:

[0029] For multi-equilibrium variable modal systems Assume constants λ>0 and μ≥1, define the region in, and R are given constants;

[0030] Assume that the Lyapunov function and two Class functions k1 and k2 such that,

[0031]

[0032] V i (x)≤μ xj (x) (6)

[0033] in, Represents a collection of modalities;

[0034]

[0035] The average residence time τ of a multi-equilibrium variable mode system a The modal signal satisfying formula (8) is globally consistent and asymptotically stable, and has a stable region Ω e ;

[0036]

[0037] in, is the bound that the average residence time needs to meet;

[0038] The initial state x(0) is outside the stable region;

[0039] Assume t0 = 0, and Expressed as the variable mode moment on the interval [0, T); for In each interval have,

[0040]

[0041] According to formula (6), we can get:

[0042]

[0043] According to formula (9) and formula (10), we can get:

[0044]

[0045] From i=0 to i=N σ (T, 0)-1 iterations, we can get:

[0046]

[0047] Among them, N0 represents the threshold value when the system switches, which is used to ensure the minimum number of times the system remains in the mode after switching to the new mode;

[0048] If the average residence time τ a If formula (8) is satisfied, the state will eventually converge to the stable region.

[0049] Furthermore, in step S300, it specifically includes:

[0050] S310, For a multi-equilibrium variable modal system, let constants λ>0, μ≥1 and γ i >0 and define the area in, and R are given constants;

[0051] Hypothesis Function and two Functions k1 and k2 such that,

[0052]

[0053] V i (x)≤μV j (x) (14)

[0054] in,

[0055] And right Can get,

[0056]

[0057] in,

[0058] Then the multi-equilibrium variable mode system is globally uniformly asymptotically stable under the variable mode signal with the average residence time satisfying formula (8), and has a stability of no more than γ * The unweighted L2 gain of

[0059]

[0060] S320. Based on the L2 gain condition of the multi-equilibrium variable modal system in step S310, a bounded real lemma in the form of a linear matrix inequality is proposed:

[0061] For a multi-equilibrium variable modal system, let λ>0, μ≥1, η>1 and γ i >0 are given constants; if the constant ∈ i ≥0 and positive definite matrix P i >0, So that,

[0062] P i ≤μP j (17)

[0063]

[0064] in,

[0065] Then the multi-equilibrium point variable mode system is globally consistent and asymptotically stable in the stable region for the variable mode signal that satisfies formula (8), and has formula (16) that does not exceed γ * The unweighted L2 gain of

[0066]

[0067] in, is the center of the minimum covering circle of all equilibrium points; R MVH >0, is the radius of the minimum covering circle.

[0068] Furthermore, a recursive randomized algorithm is used to solve the minimum covering circle.

[0069] Furthermore, in step S400, it specifically includes:

[0070] For a multi-equilibrium variable modal system, set λ>0, μ≥1 and γ i >0 is a given constant; if there is a constant ∈ i ≥0 and matrix X i >0,W i , so that

[0071] X j ≤μX i (20)

[0072]

[0073] Where Ψ=A i X i +B i W i +(A i X i +B i W i ) T +λX i ;

[0074] Then there exists a set of modally dependent state feedback H ∞ Controller u(t) = K i x(t), so that the multi-equilibrium point variable mode system is globally consistent and asymptotically stable when the variable mode signal satisfies formula (8), and the convergence region is Ω e , and the formula (16) does not exceed γ * The unweighted L2 gain of .

[0075] The present invention provides a robust control system for a multi-equilibrium point variable modal system. The system has a program module corresponding to the above steps and executes the steps in the above robust control method for the multi-equilibrium point variable modal system when running.

[0076] The present invention provides a computer-readable storage medium storing a computer program. The computer program is configured to implement steps of a robust control method for a multi-equilibrium point variable mode system when called by a processor.

[0077] Compared with the prior art, the present invention has the following beneficial effects:

[0078] ① For a class of variable modal system models in which each subsystem has a different equilibrium point, the present invention proposes the concept of globally consistent asymptotic regional stability and provides a numerically verifiable stability criterion applicable to multi-equilibrium variable modal systems. The stability analysis method adopted in the present invention extends the existing research on common equilibrium point variable modal systems to the more general multi-equilibrium point case, thus expanding the scope of application of stability analysis and controller design methods for variable modal systems.

[0079] ② In order to cope with the external interference problems encountered in actual control systems, the designed H∞ controller significantly improves the robustness of the variable modal system; and the multi-equilibrium point H∞ variable modal control method proposed in this invention improves the system's resistance to external interference, improves the safety and reliability of the control system, and has high engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 Flowchart of a robust control method for a multi-equilibrium point variable mode system according to an embodiment of the present invention;

[0081] Figure 2 Schematic diagram of the state trajectory of a multi-equilibrium variable modal system with GUARS guarantee in an embodiment of the present invention, where GUARS is globally consistent asymptotic regional stability;

[0082] Figure 3 Schematic diagram of solving the minimum covering circle of all equilibrium points of a multi-equilibrium point variable modal system in an embodiment of the present invention;

[0083] Figure 4 This is a diagram of a variable mode signal used in a simulation experiment in an embodiment of the present invention;

[0084] Figure 5 The multi-balance point variable mode controller and the multi-balance point H in the embodiment of the present invention when the system has interference ∞ State response comparison curve of variable mode controller, where x1 and x2 represent the two state variables of the system respectively;

[0085] Figure 6 1 is a graph comparing deviations between measured outputs and current balanced outputs of the multi-balance point variable modal controller and the multi-balance point H∞ variable modal controller when interference exists in the system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0086] In the description of the present invention, it should be noted that the terminology in each embodiment, such as "up", "down", "front", "back", "left", "right", etc., which indicate directions, are only for simplifying the description of the positional relationship based on the drawings in the specification, and do not mean that the referred elements and devices must be operated in accordance with the specific directions and defined operations and methods and structures in the specification. Such directional nouns do not constitute a limitation to the present invention.

[0087] In the description of the present invention, it should be noted that the terms "first," "second," and "third" mentioned in the embodiments of the present invention are used for descriptive purposes only and are not to be understood as indicating or implying relative importance or implicitly specifying the number of the technical features indicated. Therefore, a feature specified as "first," "second," or "third" may explicitly or implicitly include one or more of such features.

[0088] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0089] Specific implementation plan 1: Combined Figures 1 to 3 As shown, the present invention provides a robust control method for a multi-equilibrium point variable mode system, comprising the following steps:

[0090] S100, establishing a control system model for a multi-equilibrium-point variable modal system, including: describing the multi-equilibrium-point variable modal system as a multi-equilibrium-point variable modal system with multiple equilibrium points and external disturbances, and then expanding the existing definitions of stability and L2 gain of the variable modal system to accommodate the multi-equilibrium-point situation, specifically including:

[0091] S110. Consider the following multi-equilibrium variable modal system model:

[0092]

[0093] in, is the state vector, is the control input vector, is the measurement output vector, w is the disturbance input vector belonging to L2[0,∞); σ(t)=i is the variable mode signal, indicating that mode i is currently activated;

[0094] and Represent the equilibrium state, balanced input and balanced output of mode i respectively; A is the state matrix; B is the input matrix; C is the output matrix; D is the direct transfer matrix; E is the interference input matrix; F is the interference output matrix;

[0095] S120. Give the stability definition of a multi-equilibrium point variable modal system: For a multi-equilibrium point variable modal system If there exists a positive constant δ and a KL-like function β such that for all variable modal signals σ, the solution of the system satisfies Then the multi-equilibrium variable modal system is called globally uniform asymptotically stable (GUARS);

[0096]

[0097] in

[0098]

[0099] n represents the dimension of the state vector x, and R are Ω e The center and radius of

[0100] S130. Define the L2 gain of a multi-equilibrium point variable mode system: For a multi-equilibrium point variable mode system, if under the initial condition x(t0), for The following inequality holds:

[0101]

[0102] in represents the deviation between the measured output and the current balanced output; C is a positive constant related to x(t0); the multi-equilibrium point variable mode system is said to have an unweighted L2 gain γ; T represents the matrix transpose;

[0103] S200. Propose a stability criterion to evaluate the stability of a multi-equilibrium variable modal system, including: assigning a Lyapunov function about the center of the convergence region to each equilibrium point based on the multi-Lyapunov function method, and then giving a criterion for global consistent asymptotic regional stability based on the rate of change of the Lyapunov function. The stability of the multi-equilibrium variable modal system under the condition of average residence time is evaluated by this criterion, specifically including:

[0104] According to Theorem 1: Consider a multi-equilibrium variable modal system Assume constants λ>0 and μ≥1, define the region in, and R are given constants;

[0105] Suppose there exists a Lyapunov function ( represents a set of modes) and two Class functions k1 and k2 such that,

[0106] right

[0107]

[0108] V i (x)≤μV j (x) (6)

[0109] And right

[0110]

[0111] The average residence time τ of a multi-equilibrium variable mode system a The modal signal GUARS satisfies formula (8) and has a stable region Ω e ;

[0112]

[0113] It can be shown that, considering the initial state x(0) is outside the stable region;

[0114] Assume t0 = 0, and let represents the variable mode moment on the interval [0, T); for In each interval have,

[0115]

[0116] According to formula (6), we can get:

[0117]

[0118] According to formulas (9) and (10), we can get:

[0119]

[0120] From i=0 to i=N σ (T, 0)-1 iterations, we can get

[0121]

[0122] Where N0 represents a threshold when considering the system switching behavior, which is used to ensure that the system stays in the new mode at least a minimum number of times after switching to the new mode; if the average dwell time condition is met, the system GUARS can be guaranteed;

[0123] The state trajectory of the multi-equilibrium variable modal system with GUARS guarantee is as follows: Figure 2 As shown, the state trajectory starts from x(0) and evolves towards the equilibrium point of the currently activated mode; when the average residence time condition is met, the state eventually converges to the stable region;

[0124] S300, establishing an L2 gain analysis method for a multi-equilibrium-point variable modal system, including: first, based on the L2 gain analysis method for a multi-equilibrium-point variable modal system and the influence of variable modal and multi-equilibrium-point characteristics on the system L2 gain, and based on the L2 gain analysis results, proposing a bounded real lemma in the form of a linear matrix inequality, specifically including:

[0125] S310, according to Theorem 2: Consider the multi-equilibrium point variable modal system, that is, formula (1), set constants λ>0, μ≥1 and γ i >0 and define the area in and R are given constants;

[0126] Assume there is a function and two Functions k1 and k2,

[0127] Make

[0128]

[0129] V i (x)≤μV j (x) (14)

[0130] in,

[0131] And right Can get,

[0132]

[0133] in,

[0134] Then the multi-equilibrium point variable mode system is GUARS under the variable mode signal under the average residence time satisfying formula (8), and has no more than γ * The unweighted L2 gain of

[0135]

[0136] S320. Based on the L2 gain condition of the above-mentioned multi-equilibrium variable mode system, in order to ensure numerical testability, a bounded real lemma in the form of a linear matrix inequality is proposed. The bounded real lemma of the multi-equilibrium variable mode system is as follows:

[0137] According to Theorem 3: Consider a multi-equilibrium variable modal system, let λ>0, μ≥1, η>1 and γ i >0 are given constants; if there is a constant ∈ i ≥0 and positive definite matrix P i >0, So that,

[0138] for

[0139] P i ≤μP j (17)

[0140]

[0141] Then the multi-equilibrium variable mode system has an average residence time τ a The modal signal that satisfies formula (8) is GUARS in the stable region and has formula (16) not exceeding γ * The unweighted L2 gain of

[0142]

[0143] in, is the center of the minimum covering circle of all equilibrium points, R MVH >0, is the radius of the minimum covering circle;

[0144] The schematic diagram of solving the minimum covering circle of all equilibrium points is as follows Figure 3 As shown in the figure, the solution of the minimum covering circle adopts a recursive randomized algorithm; the basic idea is to solve the minimum covering circle on a smaller subset of equilibrium points, so that a small adjustment of this solution can cover the entire set of equilibrium points; the basic steps of the algorithm are as follows: ① Basic case, if the point set is empty or a circle containing three or fewer equilibrium points has been found, then these equilibrium points are directly used to calculate the minimum circle; ② Recursive step, randomly select a point p, assuming that the minimum covering circle of other points has been calculated, then point p is already in this circle, then it is the minimum covering circle of the entire set of equilibrium points; otherwise, point p must be on the boundary of the new minimum covering circle;

[0145] S400. Based on the bounded real lemma of multi-equilibrium variable modal system, design a modal-dependent state feedback H∞ variable modal controller for multi-equilibrium variable modal system, specifically including:

[0146] According to Theorem 4: For a multi-equilibrium variable modal system, let λ>0, μ≥1 and γi>0 be given constants. If there exists a constant ∈ i ≥0 and matrix X i >0,W i , so that for

[0147] X j ≤μX i (20)

[0148]

[0149] Where Ψ=A i X i +B i W i +(A i X i +B i W i ) T +λX i , then there exists a set of modally dependent state feedback H ∞ Controller u(t) = K i x(t), so that the multi-equilibrium point variable mode system is GUARS when the variable mode signal satisfies formula (8), and the convergence region is Ω e , and has formula (16) not exceeding γ * The unweighted L2 gain of .

[0150] Specific implementation scheme 2: The present invention provides a robust control system for a multi-equilibrium point variable modal system. The system has a program module corresponding to the above steps, and executes the steps in the above-mentioned robust control method for a multi-equilibrium point variable modal system during operation.

[0151] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0152] Specific implementation scheme three: The present invention provides a computer-readable storage medium, which stores a computer program. The computer program is configured to implement the steps of a robust control method for a multi-equilibrium point variable modal system when called by a processor.

[0153] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0154] Simulation experiment

[0155] A two-dimensional multi-equilibrium variable modal system with external disturbance is simulated. The external disturbance signal of the system is w = 30sin(0.5t)exp(-0.15t). First, a multi-equilibrium variable modal controller is designed based on Theorem 1 in step S200. Then, Theorem 4 is used to design the multi-equilibrium H ∞ Variable mode controller, this controller takes the anti-interference ability of the system into consideration during the design process, and enhances the robustness of the control system by optimizing the design of the non-weighted L2 gain. Both controllers are applied to the simulation numerical examples for testing. Figure 4 The figure shows the average residence time variable mode signal used in the simulation. In the simulation results, the multi-balance point variable mode controller and the multi-balance point H are recorded. ∞ The state response curve and output curve of the variable mode controller. Among them, the state response curve is as follows Figure 5 shown. Figure 6 The deviation between the measured output and the balanced output is given. At the moment of mode change, the deviation between the measured output and the balanced output has a momentary jump, which is mainly due to the instantaneous change of the balanced output. In addition, compared with the multi-balance point variable mode controller, the multi-balance point H ∞ The variable mode controller, which takes anti-interference performance into consideration during its design, exhibits superior robustness, especially in suppressing periodic external interference. Simulation results verify the effectiveness and advantages of the description method adopted by the present invention.

[0156] Although the present invention is disclosed as above, the scope of protection disclosed by the present invention is not limited thereto. Those skilled in the art of the present invention may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A robust control method for a multi-equilibrium variable modal system, characterized in that: The following steps are involved: S100. Establish a control system model for a multi-equilibrium-point variable modal system, describe the multi-equilibrium-point variable modal system as a multi-equilibrium-point variable modal system with multiple equilibrium points and external disturbances, and then expand the existing definitions of stability and L2 gain for variable modal systems; specifically, the following steps are included: S110, the multi-equilibrium point variable modal system model is: in, is the state vector; is the control input vector; is the measurement output vector; w is the disturbance input vector belonging to L2[0,∞); σ(t)=i is the variable mode signal, indicating that mode i is currently activated; A is the state matrix; B is the input matrix; C is the output matrix; D is the direct transfer matrix; E is the disturbance input matrix; F is the disturbance output matrix; and represent the equilibrium state, balanced input, and balanced output of mode i respectively; S120. The stability of the expanded multi-equilibrium variable modal system is defined as: For a multi-equilibrium variable modal system If there exists a positive constant δ and a KL-like function β such that for all variable modal signals σ, the solution of the system satisfies Then the multi-equilibrium point variable mode system is globally consistent and asymptotically stable: in, n represents the dimension of the state vector x; and R are Ω e The center and radius of S130. The L2 gain of the expanded multi-equilibrium point variable modal system is defined as: For a multi-equilibrium variable mode system, if the initial condition is x(t0), for If the following inequality holds, then the multi-equilibrium variable mode system has an unweighted L2 gain γ: in, represents the deviation between the measured output and the current balanced output; C is a positive constant related to x(t0); S200. Based on the multi-Lyapunov function method, a Lyapunov function about the center of the convergence region is assigned to each mode with different equilibrium points. According to the rate of change of the Lyapunov function, a criterion for global consistent asymptotic regional stability is given. The stability of the multi-equilibrium variable mode system under the condition of average residence time is evaluated by this criterion. S300. Based on the influence of variable mode and multi-equilibrium point characteristics on the L2 gain performance index of the multi-equilibrium point variable mode system, an L2 gain analysis method for the multi-equilibrium point variable mode system is established, and then a bounded real lemma in the form of a linear matrix inequality is proposed; S400, according to the bounded real lemma in the form of linear matrix inequality proposed in step S300, design the H of the mode-dependent state feedback of the multi-equilibrium point variable mode system ∞ Variable mode controller.

2. The robust control method for a multi-equilibrium point variable mode system according to claim 1, characterized in that: In step S200, it specifically includes: For multi-equilibrium variable modal systems Assume constants λ>0 and μ≥1, define the region in, and R are given constants; Assume that the Lyapunov function and two Class functions k1 and k2 such that, V i (x)≤μV j (x) (6) in, Represents a collection of modalities; The average residence time τ of a multi-equilibrium variable mode system a The modal signal satisfying formula (8) is globally consistent and asymptotically stable, and has a stable region Ω e ; in, is the bound that the average residence time needs to meet; The initial state x(0) is outside the stable region; Assume t0 = 0, and Expressed as the variable mode moment on the interval [0, T); for In each interval have, According to formula (6), we can get: According to formula (9) and formula (10), we can get: From i=0 to i=N σ (T, 0)-1 iterations, we can get: Among them, N0 represents the threshold value when the system switches, which is used to ensure the minimum number of times the system remains in the mode after switching to the new mode; If the average residence time τ a If formula (8) is satisfied, the state will eventually converge to the stable region.

3. The robust control method for a multi-equilibrium point variable mode system according to claim 2, characterized in that: In step S300, it specifically includes: S310, for a multi-equilibrium variable modal system, let constants λ>0, μ≥1 and γ i >0 and define the area in, and R are given constants; Hypothesis Function and two Functions k1 and k2 such that, V i (x)≤μV j (x) (14) in, And right Can get, in, Then the multi-equilibrium variable mode system is globally uniformly asymptotically stable under the variable mode signal with the average residence time satisfying formula (8), and has a stability of no more than γ * The unweighted L2 gain of S320. Based on the L2 gain condition of the multi-equilibrium variable modal system in step S310, a bounded real lemma in the form of a linear matrix inequality is proposed: For a multi-equilibrium variable modal system, let λ>0, μ≥, η>1 and γ i >0 are given constants; if the constant ∈ i ≥0 and positive definite matrix P i >0, So that, P i ≤μP j (17) in, Then the multi-equilibrium point variable mode system is globally consistent and asymptotically stable in the stable region for the variable mode signal that satisfies formula (8), and has formula (16) that does not exceed γ * The unweighted L2 gain of in, is the center of the minimum covering circle of all equilibrium points; R MVH >0, is the radius of the minimum covering circle.

4. The robust control method for a multi-equilibrium-point variable modal system according to claim 3, characterized in that: The solution to the minimum covering circle adopts a recursive randomized algorithm.

5. The robust control method for a multi-equilibrium point variable mode system according to claim 3, characterized in that: In step S400, it specifically includes: For a multi-equilibrium variable modal system, set λ>0, μ≥1 and γ i >0 is a given constant; if there is a constant ∈ i ≥0 and matrix X i >0,W i , so that X j ≤μX i (20) where, Ψ = A i X i + B i W i +(A i X i + B i W i ) T + λX i ; Then there exists a set of modally dependent state feedback H ∞ Controller u(t) = K i x(t), so that the multi-equilibrium point variable mode system is globally consistent and asymptotically stable when the variable mode signal satisfies formula (8), and the convergence region is Ω e , and the formula (16) does not exceed γ * The unweighted L2 gain of .

6. A robust control system for a multi-equilibrium point variable modal system, characterized by: The system has a program module corresponding to the steps of any one of claims 1 to 5, and executes the steps of the robust control method of the multi-equilibrium point variable mode system when running.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of the robust control method for a multi-equilibrium point variable mode system according to any one of claims 1 to 5 when called by a processor.

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