A method, system, and storage medium for nonlinear discrete generalized switched system control with edge-dependent average dwell time

Abstract

The application discloses a nonlinear discrete generalized switching system control method with edge-dependent average dwell time, a system and a storage medium, relates to the technical field of switching system control, and aims at solving the problems that the existing method models a switching signal as having average dwell time or mode-dependent average dwell time, ignores the edge-dependent characteristics of the switching signal, causes the controller design to be conservative when facing a switching system with a directed dwell time characteristic, and reduces system stabilizability and closed-loop system performance. The application comprises the following steps: step one, constructing a discrete nonlinear generalized switching system state space expression with edge-dependent average dwell time; step two, giving a condition for the existence of a unique solution of an open-loop system of the discrete nonlinear generalized switching system; step three, giving a dwell time condition for the open-loop system of the discrete nonlinear generalized switching system to meet exponential stability; and step four, selecting a system performance index and designing a controller of a closed-loop system.

Description

Technical Field

[0001] This invention relates to the field of switching system control technology, and more specifically, to a control method, system, and storage medium for a nonlinear discrete generalized switching system with edge-dependent average dwell time. Background Technology

[0002] Since its inception, the theory and switching methods of generalized switched systems have yielded fruitful results. Their stability proof capabilities cover not only dynamic systems described by both differential and algebraic equations, but also hybrid systems switching between multiple such subsystems. Therefore, they are widely used in control systems such as robot control, circuit control, and chemical process control. In real-world environments, these control systems often experience external disturbances caused by measurement noise and changes in the external environment, as well as system nonlinearities arising from the performance characteristics of components or actuators. Furthermore, in the digitalization and engineering implementation of practical control systems, the dynamic model of the controlled object and the digital controller often need to be analyzed and designed in the discrete time domain. This makes the controller design method for nonlinear discrete generalized switched systems highly significant in both theoretical research and engineering implementation.

[0003] In the design of controllers for such switching systems, the Lyapunov function method is widely used to derive stability and stabilization conditions for switching control systems due to its ability to measure the energy change characteristics of dynamic systems. Within this framework, existing switching controller design methods can be categorized into three types based on the characteristics of the system switching signal: those without switching signal dwell time requirements, those with average dwell time requirements, and those with mode-dependent average dwell time requirements. Comparatively, switching controller design methods with mode-dependent average dwell time requirements, due to their more accurate description of the system's switching signal, derive system stability criteria with lower conservatism and are easier to solve. However, for the more broadly defined edge-dependent average dwell time method, which describes the relationship between the current subsystem's mode-dependent average dwell time and the previously activated subsystem, the design of corresponding nonlinear discrete generalized switching system controllers is more challenging and has received little research. Summary of the Invention

[0004] The technical problem to be solved by this invention is:

[0005] Existing methods model switching signals as having average dwell time or modally dependent average dwell time, ignoring the edge dependence characteristics of switching signals. This leads to a more conservative controller design when dealing with switching systems with directed dwell time characteristics, resulting in reduced system stability and closed-loop system performance.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0007] This 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 the state-space expression for a discrete nonlinear generalized switching system with edge-dependent average dwell time;

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

[0010] Step 3: Determine the dwell time condition for the open-loop system of the discrete nonlinear generalized switching system with edge-dependent average dwell time to satisfy exponential stability.

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

[0012] Furthermore, in step one, the state-space expression of the discrete nonlinear generalized switching system with edge-dependent average dwell 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 These represent the system's state, control input, and measurable output, respectively. For energy-constrained external perturbations; δ(k) is a piecewise right-continuous constant function that maps 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 in the time interval [k l ,k l+1 ) is activated within; sampling time k l and k l+1 The time interval between them is the stay time; A i B i B ω,i and C i It is the system matrix of the i-th subsystem. It is a singular matrix, i.e., rank(E)i ) = n i ≤n; unknown nonlinear function f δ(k) (x(k)): It 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 The matrix used to describe the nonlinear characteristics of the i-th subsystem is positive semidefinite and decomposed into matrix G. δ(k) The product of its transpose, i.e.

[0018] For any switching signal δ(k), let T represents the number of switches from subsystem j to subsystem i within the time interval [k0, k). j,i (k0,k) represents the total duration of the transition from subsystem j to subsystem i within the time interval [k0,k); if a positive value exists... and It is called a property if the following conditions are met. The average marginal dependency dwell time of δ(k):

[0019]

[0020] Furthermore, in step two, the condition for the existence of a unique solution for the open-loop system of the discrete nonlinear generalized switching system is given, specifically:

[0021] For the discrete nonlinear generalized switching system with edge-dependent average dwell time described in step one, for a given scalar If a matrix exists and scalar Make The following conditions are true:

[0022]

[0023] in It is any column with full rank and satisfying The matrix has:

[0024]

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

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

[0027] When the conditions in step two are met, and there exists Make The following inequalities hold:

[0028]

[0029] Where ε(j,i)∈E represents the mode switching from subsystem j to subsystem i being included in the feasible mode switching domain E, then when the marginal dependency average residence time of the system A system is globally uniformly exponentially stable when the following conditions are met:

[0030]

[0031] Furthermore, in step four, system performance indicators are selected, and a robust controller for the closed-loop system is designed, specifically as follows:

[0032] For a given scalar and Existence matrix and scalar Makes it possible for The following conditions must be met:

[0033]

[0034] in

[0035]

[0036] And non-generalized matrix and orthogonal matrix Satisfy E i =U i diag{E 1i ,0}V i T Then, in a closed-loop discrete nonlinear generalized switching system, the switching signal has an edge-dependent average dwell time. In the case of a unique solution, there is a β0-weighted H. ∞ Performance γ0, and globally consistent exponential stability; among which

[0037]

[0038] The system's state feedback controller is composed of Give;

[0039] Repeat step four to perform scalar operations. and The value is set until a feasible solution is found in the system, and the resulting robust controller meets the system performance indicators.

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

[0041] The present invention provides a computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement the steps in the control method for a nonlinear discrete generalized switching system with edge-dependent average dwell time as described in any of the above technical solutions.

[0042] Compared with the prior art, the beneficial effects of the present invention are:

[0043] This invention improves the accuracy of system switching signal description by modeling the switching signal as having an edge-dependent average dwell time, thus achieving a more universal and accurate description of switching behavior and reducing the design difficulty of the controller.

[0044] This invention improves the applicability of control systems by considering a modeling method that can more accurately describe the dynamic behavior of actual systems. It takes into account the unavoidable nonlinearity of actual switching systems, external disturbances, and the discrete system representation corresponding to the design of digital controllers, in order to solve the model error problem caused by neglecting these factors in traditional methods.

[0045] This invention improves system stability by employing H ∞ Control methods, through H, which measures the system's ability to suppress disturbances. ∞ Optimization of performance indicators effectively suppresses the impact of external interference on system performance, significantly improves the robustness of the closed-loop system, and avoids performance degradation due to poor interference suppression.

[0046] This invention has a wide range of applications. The proposed control method and theoretical framework are applicable to various discrete generalized switching systems such as UAVs, unmanned vehicles, multimodal robots, and electronic power systems, demonstrating high application value and promotion potential. Attached Figure Description

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

[0048] Figure 2 This is the 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 This is a data graph showing the disturbances experienced by the closed-loop system composed of the controller and the nonlinear discrete generalized switching system in the embodiments of the present invention, the system output, and the numerical relationship between the two over time.

[0050] Figure 4 This is a schematic diagram comparing the control effects in embodiments of the present invention; the shaded areas represent the corresponding methods 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 These represent the minimum marginal dependency average dwell time when entering subsystems 1, 2, and 3 from other subsystems, respectively;

[0051] Figure 5 The flowchart shows the design procedure for a nonlinear discrete generalized switching system controller with edge-dependent average dwell time in an embodiment of the present invention.

[0052] Figure 6 This is a schematic diagram of a class of air-ground cross-domain platform-manipulator hybrid robots belonging to a nonlinear discrete generalized switching system with edge-dependent average dwell time.

[0053] Figure 7 This image shows the posture stabilization effect of the air-ground cross-domain platform-robotic arm composite robot under the control method proposed in this invention. Detailed Implementation

[0054] To enable those skilled in the art to better understand the present invention, exemplary embodiments or examples of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described embodiments or examples are merely some, not all, of the embodiments or examples of the present invention. All other embodiments or examples obtained by those skilled in the art based on the embodiments or examples of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0055] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0056] like Figure 5 As shown, this 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 the expression for a discrete nonlinear generalized switching system with edge-dependent average dwell time 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 These represent the system's state, control input, and measurable output, respectively. For energy-constrained external perturbations; δ(k) is a piecewise right-continuous constant function, called the switching signal, which maps 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 in the time interval [k l ,k l+1 ) is activated within; sampling time k l and k l+1 The time interval between them is the stay time; A i B i B ω,i and C i It is the system matrix of the i-th subsystem, with appropriate dimensions. It is singular, i.e., rank(E) i ) = n i ≤n; unknown nonlinear function f δ(k) (x(k)): It 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 The matrix used to describe the nonlinear characteristics of the i-th subsystem is positive semidefinite and decomposed into matrix G. δ(k) The product of its transpose, i.e.

[0063] The nonlinear generalized switching system is considered to have an average dwell time between subsystems that is not only mode-dependent but also edge-dependent. For the purpose of performing subsequent steps, the edge-dependent average dwell time is described as follows:

[0064] For any switching signal δ(k), let T represents the number of switches from subsystem j to subsystem i within the time interval [k0, k). j,i (k0,k) represents the total duration of the transition from subsystem j to subsystem i within the time interval [k0,k); if a positive value exists... and It is called a property if the following conditions are met. The average marginal dependency dwell time of δ(k):

[0065]

[0066] Step 2: Give the condition that the open-loop system of the discrete nonlinear generalized switching system has a unique solution, specifically:

[0067] For the discrete nonlinear generalized switching system with edge-dependent average dwell time described in step one, for a given scalar If a matrix exists and scalar Make The following conditions are true:

[0068]

[0069] in It is any column with full rank and satisfying The matrix has:

[0070]

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

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

[0073] definition in It is f i (x(k)) in The derivative at x = 0 is used to derive... Based on this, we can know from formula (4):

[0074]

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

[0076]

[0077] In addition, definition

[0078]

[0079] in According to E i T S i =0 and rank(S) i )=nn i Then it is concluded Right and wrong are not in a broad sense, and there are

[0080]

[0081] Therefore, by multiplying the matrix on both sides of formula (6) and N i ,get prove Right and wrong are not defined in a broad sense, therefore It is regular and causal, and the discrete nonlinear generalized switching system (1) has a unique solution in its open-loop system. The proof is complete.

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

[0083] When the conditions in step two are met, and there exists Make The following inequalities hold:

[0084]

[0085] Where ε(j,i)∈E represents the mode switching from subsystem j to subsystem i being included in the feasible mode switching domain E, then when the marginal dependency average residence time of the system A system is globally uniformly exponentially stable when the following conditions are met:

[0086]

[0087] Proof: Let the multi-Lyapunov function of the switching system be... Then formulas (4) and (10) are equivalent to:

[0088]

[0089] Consider an arbitrary switching time series k0 <k1<…<k l <..., among which for By iterating through equation (12), we obtain

[0090]

[0091] Furthermore, based on the concept of average residence time for edge dependencies, we obtain

[0092]

[0093]

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

[0095]

[0096] Therefore when At that time, it was launched

[0097]

[0098] in

[0099]

[0100] Therefore, the system is globally consistent and exponentially stable, thus proving the point.

[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 Makes it possible for The following conditions must be met:

[0103]

[0104] in

[0105]

[0106] And non-generalized matrix and orthogonal matrix Satisfy E i =U i diag{E 1i ,0}V i TThen, in a closed-loop discrete nonlinear generalized switching system, the switching signal has an edge-dependent average dwell time. In the case of a unique solution, there is a β0-weighted H. ∞ Performance γ0, and globally consistent exponential stability; among which

[0107]

[0108] The system's state feedback controller is composed of Give;

[0109] Proof: From formulas (1), (12), and (19), when the condition in step four is satisfied, the closed-loop discrete nonlinear generalized switching system has the following at the times 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, it can be derived by iteratively using formula (23):

[0113]

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

[0115]

[0116] Based on the concept of average residence time for edge dependencies, it can be derived from formula (25):

[0117]

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

[0119]

[0120] This proves that when condition (22) is satisfied, the closed-loop discrete nonlinear generalized switching system (1) has β0-weighted H ∞ Performance γ0, proof complete.

[0121] By setting scalars and The value of allows the system to have a feasible solution and satisfactory dynamic performance. Since the average residence time of marginal dependencies is more universal, the feasible range of the obtained solution and the system performance are significantly improved compared with traditional methods.

[0122] The nonlinear discrete generalized switching system control method (algorithm) with edge-dependent average dwell time proposed in this invention is the underlying technical core of this invention, and various products can be derived based on the algorithm.

[0123] Based on the method proposed in this invention, a nonlinear discrete generalized switching system control system with edge-dependent average residence time is developed using a programming language. This system has program modules 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 runtime.

[0124] The developed system (software) computer program is stored on a computer-readable storage medium. This computer program is configured to implement the steps of the aforementioned control method for a nonlinear discrete generalized switching system with edge-dependent average residence time when invoked by a processor. In other words, the invention is materialized on a carrier, becoming a computer program product.

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

[0126] The computational programs (also referred to as programs, software, software applications, or code) of this invention include machine instructions of a programmable processor and 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 apparatus (e.g., disk, optical disk, memory, programmable logic device PLD) for providing machine instructions and / or data to a programmable processor, including machine-readable media that receive 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 with reference to specific embodiments.

[0128] Example 1

[0129] Consider a nonlinear discrete generalized switching system consisting of the following matrices:

[0130]

[0131]

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

[0133]

[0134] The controller is designed using step four above, with controller parameters of 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. In this case, the system... Figure 1 The switching signal and initial conditions [x1(0),x2(0),x3(0)] shown are edge-dependent average dwell time. T =[0.3,-0.5,0.1] T The state response of the closed-loop system is as follows: Figure 2 As shown, it can be seen that even with nonlinearity and disturbances within the system, the proposed controller can still effectively stabilize the discrete generalized switched system. Figure 3 As shown, under zero initial conditions, the designed controller's interference suppression capability for the closed-loop system is: The controller design requirements have been met. Figure 4 The present invention illustrates a control method for a nonlinear discrete generalized switching system with edge-dependent average residence time and a control method for a mode-dependent average residence time (i.e.,...). Figure 4 Traditional Chinese method 1) or with average dwell time (i.e. Figure 4 Compared with the nonlinear discrete generalized switching system of the traditional method 2), it has a wider range of controller design feasibility space, which reflects the advanced nature of the controller designed in this invention.

[0135] Example 2

[0136] This embodiment illustrates the effectiveness of the proposed control method using a real-world controlled object. Consider, for example... Figure 6 The illustrated type of air-to-ground dual-purpose platform-robotic arm hybrid robot has attitude control dynamic equations that conform to the definition of a nonlinear discrete generalized switching system. Its dynamic model in the air subsystem is as follows:

[0137]

[0138] Where k represents discrete time, and φ, θ, and ψ represent roll angle, pitch angle, and yaw angle, respectively. For the desired attitude trajectory, x1 = φ - φ d , x3=θ-θ d , x5=ψ-ψ d and u φ u θ and u ψ These are the roll 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) These are the moments of inertia of the robot along the x, y, and z axes, respectively. Depending on whether the dual-purpose air-ground platform-robotic arm hybrid 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 two modes exist. In this embodiment, when the switching signal δ(k) = 1, it represents that the composite robot performs airspace movement without load; when δ(k) = 2, it represents that the composite robot performs airspace movement with load; when δ(k) = 3, it represents that the composite robot performs ground-domain movement without load; and when δ(k) = 4, it represents that the composite robot performs ground-domain movement with load. This indicates the external disturbances, such as wind, experienced by the dual-purpose air-ground platform-robotic arm composite robot. It is the control input for the robot.

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

[0140] 0×x1(k+1)=x1(k) (31)

[0141] 0 × x²(k+1) = x²(k)

[0142]

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

[0144] The model parameters in the experiment were set as m = 1.63 kg, I x,1 =I x,2 =0.0166 kg·m 2 I y,1 =I y,2 =0.0105 kg·m 2 I z,1 =I z,2 =0.0159 kg·m 2 I x,3 =I x,4 =0.0153 kg·m 2 I y,3 =I y,4 =0.0087 kg·m 2 I z,3 =I z,4 =0.0146 kg·m 2 K1 = 0.133 kg·m·s -1 K2 = 0.133 kg·m·s -1 K3 = 0.018 kg·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. Furthermore, the external perturbation is set to ω(k) = 0.02[-sin(0.1πk),-cos(0.1πk),sin(0.05πk)] T In this context, treating the switching signal as a modality-dependent average dwell time or a nonlinear discrete generalized switching system with an average dwell time fails to derive a robot attitude stabilization controller that meets performance control specifications. However, the nonlinear discrete generalized switching system control method with an edge-dependent average dwell time proposed in this invention provides a more accurate description of the switching behavior of the nonlinear discrete generalized switching system, successfully stabilizing the attitude of the air-ground dual-purpose platform-manipulator hybrid robot. Its stabilization effect is as follows: Figure 7 As shown.

[0145] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A control method for a nonlinear discrete generalized switching system with edge-dependent average dwell time, characterized in that, The implementation process of the control method is as follows: Step 1: Construct the state-space expression for a discrete nonlinear generalized switching system with edge-dependent average dwell time; Step 2: Give the condition that a discrete nonlinear generalized switched open-loop system with edge-dependent average residence time has a unique solution; Step 3: Determine the residence time condition for the discrete nonlinear generalized switching open-loop system with edge-dependent average residence time to satisfy exponential stability. Step 4: Select system performance indicators and design the controller for the discrete nonlinear generalized switched closed-loop system; In step one, the state-space expression of the discrete nonlinear generalized switching system with edge-dependent average dwell time is constructed as follows: （1） in, , and These represent the system's state, control input, and measurable output, respectively. For energy-constrained external disturbances; arbitrary signal switching It is a piecewise right-continuous constant function that will discretely sample time... Mapping to a finite set Above, among which Indicates the number of subsystems; for any switching time series ,if , Then the first Each subsystem in time interval Internal activation; sampling time and The time interval between these intervals is the dwell time; , , and It is the first The system matrix of each subsystem, matrix It is a singular matrix, that is Unknown nonlinear function It is continuously differentiable and satisfies the following quadratic constraints: （2） in Used to describe the The nonlinear characteristics of each subsystem are positive semidefinite and can be decomposed into matrices. The product of its transpose, i.e. ; For any switching signal ,make Indicates the time interval Internal Subsystem Switch to Number of switching times Indicates in From subsystem within time Switch to subsystem The total duration; If positive values ​​exist and It is called a property if the following conditions are met. for Average marginal dependency dwell time: （3） In step three, the residence time condition for a discrete nonlinear generalized switched open-loop system to satisfy exponential stability is given, specifically: When the conditions in step two are met, and there exists Make , , The following inequalities hold: （10） in Represents the subsystem To subsystem The mode switching is included in the feasible mode switching domain. In the mean time of marginal dependency of the system, A system is globally uniformly exponentially stable when the following conditions are met: （11）。 2. The control method for a nonlinear discrete generalized switching system with edge-dependent average dwell time according to claim 1, characterized in that, In step two, the condition for the existence of a unique solution for the discrete nonlinear generalized switched open-loop system is given, specifically: For the discrete nonlinear generalized switching system with edge-dependent average dwell time described in step one, for a given scalar If a matrix exists and scalar , making The following conditions are true: （4） in It is any column with full rank and satisfying The matrix has: （5） Then when At that time, the system has a unique solution under the switching signal that satisfies the edge-dependent average residence time characteristic; where This represents the sum of a matrix and its transpose. This represents the variable introduced by matrix symmetry.

3. The control method for a nonlinear discrete generalized switching system with edge-dependent average dwell time according to claim 2, characterized in that, In step four, select system performance indicators and design a robust controller for the closed-loop system, specifically as follows: For a given scalar , and There exists a matrix and scalar This makes for The following conditions must be met: （19） （20） in （21） And non-generalized matrix and orthogonal matrix satisfy Then, in a closed-loop discrete nonlinear generalized switching system, the switching signal has an edge-dependent average dwell time. In the case that it has a unique solution, there is Weighted performance Furthermore, the global consistency index is stable; in （22） The system's state feedback controller is composed of Give; Repeat step four to perform scalar operations. , and The value is set until a feasible solution is found in the system, and the resulting robust controller meets the system performance indicators.

4. A control system for a nonlinear discrete generalized switching system with edge-dependent average residence 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 3 above, and executes the steps in the above-described nonlinear discrete generalized switching system control method with edge-dependent average dwell time when it is run.

5. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the control method for a nonlinear discrete generalized switching system with edge-dependent average dwell time as described in any one of claims 1 to 3.

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