Non-linear discrete generalized switching system control method and system with edge-dependent average dwell time, and storage medium

Abstract

The invention discloses a control method and system for a nonlinear discrete generalized switching system with edge-dependent average residence time, and a storage medium, relates to the technical field of switching system control, and aims to solve the problems that according to an existing method, a switching signal is modeled to have average residence time or modal-dependent average residence time, the edge-dependent characteristic of the switching signal is ignored, and the reliability of the switching signal is poor. Therefore, the problems of conservative controller design, stability of the system and performance reduction of a closed-loop system in the face of a switching system with directed residence time characteristics are solved. Comprising the following steps: step 1, constructing a discrete nonlinear generalized switching system state space expression with edge-dependent average dwell time; 2, giving a condition that an open-loop system of the discrete nonlinear generalized switching system has a unique solution; 3, providing a residence time condition that an open-loop system of the discrete nonlinear generalized switching system meets exponential stability; and 4, selecting a system performance index, and designing a controller of the closed-loop system.

Description

Technical Field

[0001] The present invention relates to the technical field of switching system control, and in particular to a control method, system and storage medium for a nonlinear discrete generalized switching system with edge-dependent average dwell time. Background Art

[0002] Since its emergence, the theory of generalized switching systems and its switching methods have achieved fruitful results. Its stability proof capability covers not only dynamic systems described by differential equations and algebraic equations, but also hybrid systems that switch between multiple such subsystems. Therefore, it is widely used in control systems such as robot control, circuit control, and chemical processes. In actual environments, such control systems often have external disturbances caused by measurement noise, changes in the external environment, and system nonlinearity caused by the performance characteristics of components or actuators. In addition, in the actual digitalization and engineering implementation of control systems, the dynamic model and digital controller of the controlled object often need to be analyzed and designed in the discrete time domain, which makes the controller design method of nonlinear discrete generalized switching systems have strong theoretical research and engineering implementation significance.

[0003] When designing controllers for such switching systems, the multi-Lyapunov function method is widely used in the derivation of stability and stabilization conditions for switching control systems because of its ability to measure the energy change characteristics of dynamic systems. Under its framework, existing switching controller design methods can be divided into the following three types according to the characteristics of the system switching signal: one is without switching signal residence time requirements, the second is with average residence time requirements, and the third is with mode-dependent average residence time requirements. In comparison, due to the more accurate description of the system switching signal, the system stability criterion derived by the switching controller design method with mode-dependent average residence time requirements is less conservative and less difficult to solve. However, for the more extensive edge-dependent average residence time method that can describe the connection between the current subsystem's mode-dependent average residence time and the previously activated subsystem, the corresponding nonlinear discrete generalized switching system controller design is difficult and rarely studied. Summary of the invention

[0004] The technical problems to be solved by the present invention are:

[0005] Existing methods model switching signals as having an average dwell time or a modally dependent average dwell time, ignoring the edge dependence characteristics of the switching signal. This results in a more conservative controller design when facing a switching system with a directed dwell time characteristic, and reduces the system's stabilization and closed-loop system performance.

[0006] The present invention adopts the following technical solutions to solve the above technical problems:

[0007] The present invention provides a control method for a nonlinear discrete generalized switching system with edge-dependent average dwell time. The implementation process of the control method is as follows:

[0008] Step 1: Construct a state space expression of a discrete nonlinear generalized switching system with edge-dependent average residence time;

[0009] Step 2: providing the condition that the discrete nonlinear generalized switching system with edge-dependent average residence time has a unique solution;

[0010] Step 3, providing a residence time condition for the open-loop system of the discrete nonlinear generalized switching system with edge-dependent average residence time to satisfy exponential stability;

[0011] Step 4: Select system performance indicators and design the controller of the closed-loop system.

[0012] Furthermore, in step 1, the state space expression of the discrete nonlinear generalized switching system with edge-dependent average residence time is constructed as follows:

[0013] E δ(k) x(k+1)=A δ(k) x(k)+B δ(k) u(k)+B ω,δ(k) ω(k)+f δ(k) (x(k)) (1)

[0014] z(k)=C δ(k) x(k)

[0015] in, and Respectively represent the state, control input and measurable output of the system; is an energy-limited external disturbance; δ(k) is a piecewise right-continuous constant function that maps the discrete sampling time k to a finite set Where N>1 represents the number of subsystems; for any switching time sequence 0≤k0 <k1<…<k l <…, if δ(k)=δ(k l )=i, Then the i-th subsystem is in the time interval [k l ,k l+1 ) is activated; sampling time k l and k l+1 The time interval between is the dwell time; i , B i , B ω,i and C i is the system matrix of the ith subsystem, the matrix Is a singular matrix, that is, rank(Ei )=n i ≤n; unknown nonlinear function f δ(k) (x(k)): is continuously differentiable and satisfies the following quadratic constraints:

[0016] f δ(k) (x(k)) T f δ(k) (x(k))≤x T (k)H δ(k) x(k) (2)

[0017] in It is used to describe the nonlinear characteristics of the ith subsystem, is semi-positive definite, and is decomposed into the matrix G δ(k) The product of its transpose, that is

[0018] For any switching signal δ(k), let represents the number of switches from subsystem j to i in the time interval [k0, k), T j,i (k0,k) represents the total duration of the transition from subsystem j to subsystem i within the time [k0,k); if there is a positive value and If the following conditions are met, it is called is the average edge-dependent dwell time of δ(k):

[0019]

[0020] Furthermore, in step 2, the conditions for the existence of a unique solution for the discrete nonlinear generalized switched system open-loop system are given, specifically:

[0021] For the discrete nonlinear generalized switching system with edge-dependent average dwell time described in step 1, for a given scalar If there is a matrix And scalar Make The following conditions hold:

[0022]

[0023] in is any full column rank satisfying 's matrix, and we have:

[0024]

[0025] Then when ω(k)≡0, the system has a unique solution under the switching signal that satisfies the edge-dependent average dwell time characteristic; where <·> srepresents the sum of a matrix and its transpose, and * represents a variable introduced by the symmetry of the matrix.

[0026] Furthermore, in step three, the dwell time condition for the open-loop system of the discrete nonlinear generalized switching system to satisfy exponential stability is given, which is specifically:

[0027] When the conditions of step 2 are met and there is Make The following inequality holds:

[0028]

[0029] Where ε(j,i)∈E represents that the mode switching from subsystem j to subsystem i is included in the feasible mode switching domain E. When the edge dependence average residence time of the system A system is globally consistent exponentially stable if the following conditions are met:

[0030]

[0031] Furthermore, in step 4, the system performance index is selected and the robust controller of the closed-loop system is designed, specifically:

[0032] For a given scalar and Existence Matrix and scalar Make for The following conditions hold:

[0033]

[0034] in

[0035]

[0036] And the non-generalized matrix and orthogonal matrix Satisfy E i =U i diag{E 1i ,0}V i T , then the closed-loop discrete nonlinear generalized switching system has an edge-dependent average dwell time when the switching signal There is a unique solution in the case of β0 weighted H ∞ The performance is γ0, and the global consistency index is stable;

[0037]

[0038] The state feedback controller of the system is given by given;

[0039] Repeat step 4 to perform scalar and The value is set until there is a feasible solution in the guarantee system and the obtained robust controller meets the system performance indicators.

[0040] The present invention provides a nonlinear discrete generalized switching system control system with edge-dependent average residence time. The system has a program module corresponding to the steps of the method described in any one of the above technical solutions, and executes the steps in the above-mentioned nonlinear discrete generalized switching system control method with edge-dependent average residence time during operation.

[0041] The present invention provides a computer-readable storage medium, which stores a computer program. The computer program is configured to implement the steps in the control method of a nonlinear discrete generalized switching system with an edge-dependent average residence time described in any one of the above-mentioned technical solutions when called by a processor.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] The present invention improves the accuracy of describing the system switching signal, and achieves a more universal and accurate description of the switching behavior by modeling the switching signal as having an edge-dependent average residence time, thereby reducing the difficulty of designing the controller.

[0044] The present invention improves the applicability of the control system and considers a type of modeling method that can more accurately describe the dynamic behavior of the actual system. It takes into account the inevitable nonlinearity and external disturbances of the actual switching system and the discrete system representation corresponding to the designed digital controller, so as to solve the model error problem caused by ignoring these factors in the traditional method.

[0045] The present invention improves the system stability and adopts H ∞ The control method measures the disturbance suppression capability of the system by ∞ The performance indicators are optimized, so that the impact of external interference on system performance is effectively suppressed, the robustness of the closed-loop system is effectively improved, and the degradation of system performance due to poor interference suppression effect is avoided.

[0046] The present invention has a wide range of applications. The proposed control method and theoretical framework are suitable for various discrete generalized switching systems such as drones, unmanned vehicles, multimodal robots, and electronic power systems, showing high application value and promotion potential. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is a schematic diagram of a switching function with edge-dependent average dwell time in an embodiment of the present invention;

[0048] Figure 2 is a closed-loop system state response diagram of a nonlinear discrete generalized switching system with edge-dependent average dwell time in an embodiment of the present invention;

[0049] Figure 3 A data graph showing the disturbance to a closed-loop system constituted by a controller and a nonlinear discrete generalized switching system in an embodiment of the present invention, the system output, and the numerical relationship between the two changing over time;

[0050] Figure 4 Schematic diagram of control effect comparison in the embodiment of the present invention; the shaded part represents the corresponding method in the corresponding t j,1 , t j,2 and t j,3 The parameters can meet the controller design requirements, among which t j,1 , t j,2 and t j,3 They represent the minimum edge-dependent average residence time when entering subsystems 1, 2, and 3 from other subsystems;

[0051] Figure 5 A flow chart of a program design for a nonlinear discrete generalized switching system controller with edge-dependent average dwell time in an embodiment of the present invention;

[0052] Figure 6 Schematic diagram of a type of air-ground cross-domain platform-manipulator composite robot belonging to a nonlinear discrete generalized switching system with edge-dependent average dwell time;

[0053] Figure 7 This is a diagram showing the posture stabilization effect of the air-to-ground cross-domain platform-robotic arm composite robot under the control method proposed in the present invention. DETAILED DESCRIPTION

[0054] In order to enable those skilled in the art to better understand the scheme of the present invention, exemplary implementations or embodiments of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described implementations or embodiments are only implementations or embodiments of a part of the present invention, not all of them. Based on the implementations or embodiments of the present invention, all other implementations or embodiments obtained by ordinary technicians in the field without creative work should fall within the scope of protection of the present invention.

[0055] 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.

[0056] like Figure 5 As shown, the present invention provides a control method for a nonlinear discrete generalized switching system with edge-dependent average dwell time, comprising the following steps:

[0057] Step 1: Construct a discrete nonlinear generalized switching system with edge-dependent average dwell time. The expression is as follows:

[0058] E δ(k) x(k+1)=A δ(k) x(k)+B δ(k) u(k)+B ω,δ(k) ω(k)+f δ(k) (x(k)) (1)

[0059] z(k)=C δ(k) x(k)

[0060] in, and Respectively represent the state, control input and measurable output of the system; is an energy-limited external disturbance; δ(k) is a piecewise right-continuous constant function, called a switching signal, which maps the discrete sampling time k to a finite set Where N>1 represents the number of subsystems; for any switching time sequence 0≤k0 <k1<…<k l <…, if δ(k)=δ(k l )=i, Then the i-th subsystem is in the time interval [k l ,k l+1 ) is activated; sampling time k l and k l+1 The time interval between is the dwell time; i , B i , B ω,i and C i is the system matrix of the ith subsystem, with appropriate dimensions, the matrix is singular, that is, rank(E i )=n i ≤n; unknown nonlinear function f δ(k) (x(k)): is continuously differentiable and satisfies the following quadratic constraints:

[0061] f δ(k) (x(k)) T f δ(k) (x(k))≤x T (k)H δ(k) x(k) (2)

[0062] in It is used to describe the nonlinear characteristics of the ith subsystem, is semi-positive definite, and is decomposed into the matrix G δ(k) The product of its transpose, that is

[0063] The nonlinear generalized switching system is considered to have an average residence time between switching subsystems that is not only mode-dependent but also edge-dependent. To perform the subsequent steps, the edge-dependent average residence time is explained as follows:

[0064] For any switching signal δ(k), let represents the number of switches from subsystem j to i in the time interval [k0, k), T j,i (k0,k) represents the total duration of the transition from subsystem j to subsystem i within the time [k0,k); if there is a positive value and If the following conditions are met, it is called is the average edge-dependent dwell time of δ(k):

[0065]

[0066] Step 2: Give the conditions for the existence of a unique solution for the discrete nonlinear generalized switching system open-loop system, specifically:

[0067] For the discrete nonlinear generalized switching system with edge-dependent average dwell time described in step 1, for a given scalar If there is a matrix And scalar Make The following conditions hold:

[0068]

[0069] in is any full column rank satisfying 's matrix, and we have:

[0070]

[0071] Then when ω(k)≡0, the system has a unique solution under the switching signal that satisfies the edge-dependent average dwell time characteristic; where <·> s represents the sum of a matrix and its transpose, and * represents a variable introduced by the symmetry of the matrix;

[0072] The proof of this step is as follows:

[0073] definition in Yes i (x(k)) The derivative at x = 0, then we can deduce On this basis, we can know from formula (4):

[0074]

[0075] because And rank(E i )=n i ≤n, then there exists a non-singular matrix So that:

[0076]

[0077] In addition, the definition

[0078]

[0079] in According to E i T S i = 0 and rank(S i ) = n n i , then the is not generalized, and has

[0080]

[0081] Therefore, by multiplying the matrix left and right in formula (6) and N i ,get prove is non-generalized, so It is regular and causal. The discrete nonlinear generalized switching system (1) has a unique solution for the open-loop system. The proof is complete.

[0082] Step 3: Give the dwell time condition for the open-loop system of the discrete nonlinear generalized switching system to satisfy exponential stability, specifically:

[0083] When the conditions of step 2 are met and there is Make The following inequality holds:

[0084]

[0085] Where ε(j,i)∈E represents that the mode switching from subsystem j to subsystem i is included in the feasible mode switching domain E. When the edge dependence average residence time of the system A system is globally consistent exponentially stable if the following conditions are met:

[0086]

[0087] Proof: Assume that the multi-Lyapunov function of the switching system is Then formulas (4) and (10) are equivalent to:

[0088]

[0089] Consider an arbitrary switching time series k0 <k1<…<k l <…, where for By iterating equation (12), we get

[0090]

[0091] In addition, according to the concept of edge-dependent average residence time, we get

[0092]

[0093]

[0094] From formulas (13), (14) and (15), we can infer

[0095]

[0096] Therefore, when When the launch

[0097]

[0098] in

[0099]

[0100] Therefore, the system is globally consistent exponentially stable, and the proof is complete.

[0101] Step 4: Select system performance indicators and design a robust controller for the closed-loop system, specifically:

[0102] For a given scalar and Existence Matrix and scalar Make for The following conditions hold:

[0103]

[0104] in

[0105]

[0106] And the non-generalized matrix and orthogonal matrix Satisfy E i =U i diag{E 1i ,0}V i T, then the closed-loop discrete nonlinear generalized switching system has an edge-dependent average dwell time when the switching signal There is a unique solution in the case of β0 weighted H ∞ The performance is γ0, and the global consistency index is stable;

[0107]

[0108] The state feedback controller of the system is given by given;

[0109] Proof: It can be deduced from formulas (1), (12) and (19) that when the conditions of step 4 are met, the closed-loop discrete nonlinear generalized switching system has the following equations when the mode does not change and when the mode changes:

[0110] V(δ(k),x(k+1))-β δ(k) V(δ(k),x(k))+L(k)≤0

[0111] V(δ(k),x(k))<μ δ(k-1),δ(k) V(δ(k-1),x(k)) (23)

[0112] Where L(k) = z T (k)z(k)-γ 2 ω T (k)ω(k), then under zero initial conditions, by cyclic use of formula (23), we can derive:

[0113]

[0114] Multiply both sides of formula (24) by roll out:

[0115]

[0116] According to the concept of edge-dependent average residence time, formula (25) can be used to deduce:

[0117]

[0118] By integrating (26) from k = k0 to ∞ and then swapping the order of the summation, we obtain:

[0119]

[0120] It is proved that when condition (22) is satisfied, the closed-loop discrete nonlinear generalized switched system (1) has a β0-weighted H ∞ Performance γ0, proof completed.

[0121] By setting the scalar and The value of makes the system have a feasible solution and satisfactory system dynamic performance. Due to the stronger universality of the edge-dependent average residence time, the feasible range of the solution and the system performance are significantly improved compared with the traditional method.

[0122] The present invention proposes a nonlinear discrete generalized switching system control method (algorithm) with edge-dependent average residence time, which is the underlying technical core of the present invention. Various products can be derived based on the algorithm.

[0123] Based on the method proposed in the present invention, a nonlinear discrete generalized switching system control system with edge-dependent average residence time is developed using a programming language. The system has a program module corresponding to the steps of the above-mentioned technical solution, and executes the steps in the above-mentioned nonlinear discrete generalized switching system control method with edge-dependent average residence time during operation.

[0124] The computer program of the developed system (software) is stored on a computer-readable storage medium, and the computer program is configured to implement the steps of the above-mentioned nonlinear discrete generalized switching system control method with edge-dependent average residence time when called by a processor. That is, the present invention is materialized on a carrier to become a computer program product.

[0125] Various implementations of the systems and techniques described herein can be realized in digital electronic circuit systems, integrated circuit systems, dedicated ASICs (application specific integrated circuits), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include: being implemented in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0126] The computer programs (also referred to as programs, software, software applications, or codes) of the present invention include machine instructions for programmable processors, and these computer programs can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, device, and / or device (e.g., disk, optical disk, memory, programmable logic device PLD) for providing machine instructions and / or data to a programmable processor, including a machine-readable medium that receives machine instructions as machine-readable signals. The term "machine-readable signal" refers to any signal for providing machine instructions and / or data to a programmable processor.

[0127] The beneficial effects of the present invention will be described below in conjunction with specific embodiments.

[0128] Example 1

[0129] Consider a nonlinear discrete generalized switched system consisting of the following matrix:

[0130]

[0131]

[0132] The nonlinear term f in the system δ(k) (x(k)) and the system disturbance ω(k) are given by:

[0133]

[0134] Use the above step 4 to design the controller, and the controller parameter is μ 2,1 =1.1,μ 3,1 =1.6,μ 1,2 =1.2,μ 3,2 =1.7μ 1,3 =2.7,μ 2,3 =2.3, and β1 = 0.65, β2 = 0.75, β3 = 0.8, γ = 0.55, then the system is Figure 1 The switching signal with edge-dependent average dwell time and initial conditions [x1(0), x2(0), x3(0)] are shown T =[0.3,-0.5,0.1] T Under this condition, the state response of the closed-loop system is as follows: Figure 2 As shown in , it can be seen that the proposed controller can still effectively stabilize the discrete generalized switching system when there are nonlinearities and disturbances in the system. Figure 3 As shown in Figure 2, under zero initial conditions, the interference suppression capability of the designed controller for the closed-loop system is The design requirements of the controller are met. Figure 4 The control method of the nonlinear discrete generalized switching system with edge-dependent average residence time in the present invention is different from the control method of the nonlinear discrete generalized switching system with mode-dependent average residence time (i.e. Figure 4 The traditional method 1) or with average residence time (i.e. Figure 4 Compared with the nonlinear discrete generalized switching system of the traditional method 2), it has a wider feasible space for controller design, which reflects the advancement of the controller designed by the present invention.

[0135] Example 2

[0136] This embodiment uses a class of actual controlled objects to illustrate the effectiveness of the proposed control method. Figure 6 The figure shows a type of air-ground dual-purpose platform-manipulator composite robot. The attitude control dynamic equation of the robot conforms to the definition of a nonlinear discrete generalized switching system. Its dynamic model in the air subsystem is:

[0137]

[0138] Where k represents discrete time, φ, θ, and ψ represent the roll angle, pitch angle, and yaw angle, respectively. is the desired posture trajectory, x1=φ-φ d , x3=θ-θ d , x5=ψ-ψ d and u φ 、u θ and u ψ They are rolling thrust input, pitch thrust input and yaw moment, K i , i∈1,2,3 are aerodynamic constants, l represents the distance from the rotor to the geometric center of the aircraft, I x,δ(k) ,I y,δ(k) and I z,δ(k) are the moments of inertia of the robot along the x, y and z axes respectively. Depending on whether the air-ground dual-purpose platform-manipulator composite robot carries a payload, the moment of inertia I x,δ(k) ,I y,δ(k) and I z,δ(k) In this embodiment, it is assumed that there are two modes. In this embodiment, when the switching signal δ(k) = 1, it means that the composite robot performs airspace unloaded motion, when (k) = 2, it means that the composite robot performs airspace loaded motion, when δ(k) = 3, it means that the composite robot performs ground-domain unloaded motion, and when δ(k) = 4, it means that the composite robot performs ground-domain loaded motion. It represents the external disturbances such as wind disturbance to the air-ground dual-purpose platform-manipulator composite robot. is the control input of the robot.

[0139] Under the ground subsystem, due to the influence of ground contact on the composite robot, its dynamic model is:

[0140] 0×x1(k+1)=x1(k) (31)

[0141] 0×x2(k+1)=x2(k)

[0142]

[0143] remove Except for this, the definitions of the variables in (31) are the same as those in (30), where

[0144] The model parameters in the experiment are set as m = 1.63 kg, I x,1 =I x,2 =0.0166kg·m 2 , I y,1 =I y,2 =0.0105kg·m 2 , I z,1 =I z,2 =0.0159kg·m 2 , I x,3 =I x,4 =0.0153kg·m 2 , I y,3 =I y,4 =0.0087kg·m 2 , I z,3 =I z,4 =0.0146kg·m 2 , K1=0.133kg·m·s -1 , K2=0.133kg·m·s -1 , K3=0.018kg·s -1 , The controller parameters are β1=β2=0.99,β3=β4=0.98,γ=1.85,μ 1,2 =μ 2,1 =2.5,μ 3,4 =μ 4,3 =2.3,μ 1,3 =μ 3,1 =7.5,μ 2,4 =μ 4,2 =8.0. In addition, the external disturbance is set to ω(k) = 0.02[-sin(0.1πk),-cos(0.1πk),sin(0.05πk)] T In this case, treating the switching signal as a mode-dependent average dwell time or a nonlinear discrete generalized switching system with an average dwell time cannot derive a robot posture stabilization controller that meets the performance control index. The control method of the nonlinear discrete generalized switching system with an edge-dependent average dwell time proposed in the present invention can successfully stabilize the posture of the air-ground dual-purpose platform-manipulator composite robot because it provides a more accurate description of the switching behavior of the nonlinear discrete generalized switching system. The stabilization effect is as follows Figure 7 shown.

[0145] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art 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 protection scope of the present invention.

Claims

1. A control method for nonlinear discrete generalized switching systems with edge-dependent average dwell time, characterized in that: The implementation process of the control method is: Step 1: Construct a state space expression of a discrete nonlinear generalized switching system with edge-dependent average residence time; Step 2: providing the condition that the discrete nonlinear generalized switching system with edge-dependent average residence time has a unique solution; Step 3, providing a residence time condition for the open-loop system of the discrete nonlinear generalized switching system with edge-dependent average residence time to satisfy exponential stability; Step 4: Select system performance indicators and design the controller of the closed-loop system.

2. The control method for nonlinear discrete generalized switching systems with edge-dependent average dwell time proposed in claim 1, characterized in that: In step 1, the state space expression of the discrete nonlinear generalized switching system with edge-dependent average dwell time is constructed as follows: E δ(k) x(k+1)=A δ(k) x(k)+B δ(k) u(k)+B ω,δ(k) ω(k)+f δ(k) (x(k)) (1) z(k)=C δ(k) x(k) wherein, and respectively represent the state, control input and measurable output of the system; is an energy - limited external disturbance; δ(k) is a piece - wise right - continuous constant function that maps the discrete sampling time k to a finite set where N>1 represents the number of subsystems; for any switching time sequence 0≤k0<k1<…<kl<…, if δ(k)=δ(k l )) = i, then the i - th subsystem is activated in the time interval [k l , k l+1 ); the time interval between the sampling times k l and k l+1 is the dwell time; A i , B i , B ω,i and C i are the system matrices of the i - th subsystem, and the matrix is a singular matrix, i.e., rank(E i ) = n i ≤n; the unknown nonlinear function is continuously differentiable and satisfies the following quadratic constraint: f δ(k) (x(k)) T f δ(k) (x(k))≤x T (k)H δ(k) x(k) (2) in It is used to describe the nonlinear characteristics of the ith subsystem, is semi-positive definite, and is decomposed into the matrix G δ(k) The product of its transpose, that is For any switching signal δ(k), let represents the number of switches from subsystem j to i in the time interval [k0, k), T j,i (k0,k) represents the total duration of the transition from subsystem j to subsystem i within the time [k0,k); if there is a positive value and If the following conditions are met, it is called is the average edge-dependent dwell time of δ(k):

3. The control method for nonlinear discrete generalized switching systems with edge-dependent average dwell time according to claim 1, characterized in that: In step 2, the conditions for the existence of a unique solution for the discrete nonlinear generalized switched system open-loop system are given, specifically: For the discrete nonlinear generalized switching system with edge-dependent average dwell time described in step 1, for a given scalar If there is a matrix And scalar Make The following conditions hold: in is any full column rank satisfying 's matrix, and we have: Then when ω(k)≡0, the system has a unique solution under the switching signal that satisfies the edge-dependent average dwell time characteristic; where <·> s represents the sum of a matrix and its transpose, and * represents a variable introduced by the symmetry of the matrix.

4. A control method for a nonlinear discrete generalized switching system with edge-dependent average dwell time according to claim 1, characterized in that: In step 3, the dwell time condition for the open-loop system of the discrete nonlinear generalized switching system to satisfy exponential stability is given, which is: When the conditions of step 2 are met and there is Make i≠j, ε(j,i)∈ε, the following inequality holds: Where ∈(j,i)∈ε represents that the mode switching from subsystem j to subsystem i is included in the feasible mode switching domain ε. When the edge dependence average residence time of the system A system is globally consistent exponentially stable if the following conditions are met:

5. A control method for a nonlinear discrete generalized switching system with edge-dependent average dwell time according to claim 1, characterized in that: In step 4, select the system performance indicators and design the robust controller of the closed-loop system, specifically: For a given scalar and Existence Matrix and scalar Make for ∈(j,i)∈ε, the following conditions hold: in And the non-generalized matrix and the orthogonal matrix U i , Satisfy E i =U i diag{E 1i ,0}V i T , then the closed-loop discrete nonlinear generalized switching system has an edge-dependent average residence time when the switching signal There is a unique solution in the case of β0 weighted H ∞ The performance is γ0, and the global consistency index is stable; in The state feedback controller of the system is given by given; Repeat step 4 to perform scalar and The value is set until there is a feasible solution in the guarantee system and the obtained robust controller meets the system performance indicators.

6. A nonlinear discrete generalized switching system control system with edge-dependent average dwell time, characterized in that: The system has a program module corresponding to the steps of the method described in any one of claims 1 to 5, and executes the steps in the above-mentioned nonlinear discrete generalized switching system control method with edge-dependent average residence time 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 in the control method of a nonlinear discrete generalized switching system with edge-dependent average residence time according to any one of claims 1 to 5 when called by a processor.

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