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1.
In this paper, the problem of hybrid control strategy (HCS) for time-varying delay positive switched linear systems (PSLS) with unstable modes is studied. Firstly, the HCS, which includes minimum switching strategy and discretized state feedback controller, is applied to PSLS with time-varying delay for the first time. Secondly, by using the discretized multiple linear copositive Lyapunov-Krasovskii functional, a sufficient condition of globally uniformly asymptotically stable (GUAS) under the HCS is given. Finally, the HCS is extended to discrete-time positive switched time delay systems, and a delay independent stabilization condition is obtained in the discrete system. The effectiveness of the HCS is verified by two simulation examples.  相似文献   

2.
This paper is concerned with the problem of discrete-time event-triggered H∞ control for networked cascade control systems (NCCSs) with time-varying network-induced delay. First of all, an event-triggered scheme is introduced to this system for reducing the unnecessary waste of limited network bandwidth resources. Considering the effect of time-varying delay, a new mathematical model for this system is constructed. In this paper, based on the model and Lyapunov functional method, the co-design method of event-triggered parameter, state feedback primary controller and secondary controller with H∞ performance is derived via linear matrix inequality technique. To illustrate the effectiveness of the proposed method, a simulation example considering a main steam temperature cascade control system is given. The proposed method emphasizes the application in the corresponding industrial control systems, it can be found that this method is superior to the one in some existing references, and the provided example demonstrates the effectiveness of the co-design method in the networked cascade control systems with event-triggered scheme.  相似文献   

3.
This paper is concerned with stability analysis and stabilization of time-varying delay discrete-time systems in Lyapunov-Krasovskii stability analysis framework. In this regard, a less conservative approach is introduced based on non-monotonic Lyapunov-Krasovskii (NMLK) technique. The proposed method derives time-varying delay dependent stability conditions based on Lyapunov-Krasovskii functional (LKF), which are in the form of linear matrix inequalities (LMI). Also, a PID controller designing algorithm is extracted based on obtained NMLK stability condition. The stability of the closed loop system is guaranteed using the designed controller. Another property that is important along with the stability, is the optimality of the controller. Thus, an optimal PID designing technique is introduced in this article. The proposed method can be used to design optimal PID controller for unstable multi-input multi-output time-varying delay discrete-time systems. The proposed stability and stabilization conditions are less conservative due to the use of non-monotonic decreasing technique. The novelty of the paper comes from the consideration of non-monotonic approach for stability analysis of time-varying delay discrete-time systems and using obtained stability conditions for designing PID controller. Numerical examples and simulations are given to evaluate the theoretical results and illustrate its effectiveness compared to the existing methods.  相似文献   

4.
This paper is concerned with the problem of state feedback stabilization of a class of discrete-time switched singular systems with time-varying state delay under asynchronous switching. The asynchronous switching considered here means that the switching instants of the candidate controllers lag behind those of the subsystems. The concept of mismatched control rate is introduced. By using the multiple Lyapunov function approach and the average dwell time technique, a sufficient condition for the existence of a class of stabilizing switching laws is first derived to guarantee the closed-loop system to be regular, causal and exponentially stable in the presence of asynchronous switching. The stabilizing switching laws are characterized by a upper bound on the mismatched control rate and a lower bound on the average dwell time. Then, the corresponding solvability condition for a set of mode-dependent state feedback controllers is established by using the linear matrix inequality (LMI) technique. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.  相似文献   

5.
Finite-time stability concerns the boundness of system during a fixed finite-time interval. For switched systems, finite-time stability property can be affected significantly by switching behavior; however, it was neglected by most previous research. In this paper, the problems of finite-time stability analysis and stabilization for switched nonlinear discrete-time systems are addressed. First, sufficient conditions are given to ensure a class of switched nonlinear discrete-time system subjected to norm bounded disturbance finite-time bounded under arbitrary switching, and then the results are extended to H∞ finite-time boundness of switched nonlinear discrete-time systems. Finally based on the results on finite-time boundness, the state feedback controller is designed to H∞ finite-time stabilize a switched nonlinear discrete-time system. A numerical design example is given to illustrate the proposed results within this paper.  相似文献   

6.
This paper is concerned with state feedback stabilization of discrete-time switched singular systems with time-varying delays existing simultaneously in the state, the output and the switching signal of the switched controller. On the basis of equivalent dynamics decomposition and Lyapunov–Krasovskii method, exponential estimates for the response of slow states of the closed-loop subsystems running in asynchronous and synchronous periods are first given. Exponential estimates for the response of fast states are also provided by establishing an analytic equation to solve the fast states and using some algebraic techniques. Then, by employing the obtained exponential estimates and the piecewise Lyapunov function approach with average dwell time (ADT) switching, sufficient conditions for the existence of a class of stabilizing switching signals and state feedback gains are derived, which explicitly depend on upper bounds on the delays and a lower bound on the ADT. Finally, two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.  相似文献   

7.
This paper is concerned with the H∞ control problem for a class of networked control systems (NCSs) with time-varying delay that is less than one sampling period. By applying a new working mode of the actuator and considering state feedback controllers, a new discrete-time switched system model is proposed to describe the NCS. Based on the obtained switched system model, a sufficient condition is derived for the closed-loop NCS to be exponentially stable and ensure a prescribed H∞ performance level. The obtained condition establishes relations among the delay length, the delay variation frequency, and the system performances of the closed-loop NCS. Moreover, a convex optimization problem is formulated to design the H∞ controllers which minimize the H∞ performance level. An illustrative example is given to show the effectiveness of the proposed results.  相似文献   

8.
This paper is concerned with the exponential stabilization of switched linear systems subject to actuator saturation with both stabilizable subsystems and unstabilizable subsystems for continuous-time case and discrete-time case, respectively. Sufficient conditions for the exponential stabilization under dwell time switching under the cases of continuous-time and discrete-time are established by using a novel class of multiple time-varying Lyapunov function. The existence conditions for stabilizing controllers are presented in terms of linear matrix inequalities (LMIs) for the continuous-time case and the discrete-time case, respectively. Two optimization problems are proposed for obtaining the maximal attraction region. The problem of exponential stabilization for switched system subject to actuator saturation with asynchronous switching controller is also studied. Several numerical examples are presented to prove the validity of the obtained results.  相似文献   

9.
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10.
In this paper, we deal with the cooperative output regulation problem of linear multi-agent systems on a directed network topology subject to both stochastic packet dropout and time-varying communication delay. On the basis of introducing a queuing mechanism, a distributed state feedback control algorithm is proposed. Then the continuous-time multi-agent systems with piece-wise constant control are converted into discrete-time systems. Under some standard assumptions, the necessary and sufficient conditions under which the tracking errors of followers approach to the origin asymptotically are proposed for different exosystems. Finally, the proposed results are verified via two examples.  相似文献   

11.
《Journal of The Franklin Institute》2023,360(14):10499-10516
In this paper, we aim to study model-based event-triggered control for a class of uncertain switched discrete-time systems composed of stabilizable and unstabilizable subsystems. A nominal model is introduced at the controller side to form a dynamic controller so that it can provide a kind of approximate estimate of the system state for system input even the overall switched discrete-time system is running in open-loop during any two consecutive event-triggered instants. By using multi-Lyapunov function method and the average dwell time switching strategy, stability conditions given in linear matrix inequality form for the closed-loop switched discrete-time system are derived. The design of control gains is also given. Finally, a numerical example and a physical example are provided to verify the effectiveness and usefulness of the proposed method.  相似文献   

12.
For a continuous-time linear system with constant reference input, the network-based proportional-integral (PI) control is developed to solve the output tracking control problem by taking time-varying sampling and network-induced delays into account. A traditional PI control system is introduced to obtain the equilibriums of state and control input. Using the equilibriums, a discrete-time PI tracking controller in a network environment is constructed. The resulting network-based PI control system is described by an augmented system with two input delays and the output tracking objective is transformed into ensuring asymptotic stability of the augmented system. A delay-dependent stability condition is established by a discontinuous augmented Lyapunov–Krasovskii functional approach. The PI controller design result of in-wheel motor as a case study is provided in terms of linear matrix inequalities. Matlab simulation and experimental results resorting to a test-bed for ZigBee-based control of in-wheel motor are given to validate the proposed method.  相似文献   

13.
This paper deals with the problem of stabilization for a class of hybrid systems with time-varying delays. The system to be considered is with nonlinear perturbation and the delay is time varying in both the state and control. Using an improved Lyapunov–Krasovskii functional combined with Newton–Leibniz formula, a memoryless switched controller design for exponential stabilization of switched systems is proposed. The conditions for the exponential stabilization are presented in terms of the solution of matrix Riccati equations, which allow for an arbitrary prescribed stability degree.  相似文献   

14.
This paper is devoted to adaptive neural network control issue for a class of nonstrict-feedback uncertain systems with input delay and asymmetric time-varying state constraints. State-related external disturbances are involved into the system, and the upper bounds of disturbances are assumed as functions of state variables instead of constants. Additionally, during the approximations of unknown functions by neural networks, the online computation burdens are declined sharply, since the norms of neural network weight vectors are only estimated. In the process of dealing with input delay, an auxiliary function is applied such that the conditions for time delay are more general than the ones in existing literature. A novel adaptive neural network controller is designed by constructing the asymmetric barrier Lyapunov function, which guarantees that the output of system has a good tracking performance and the state variables never violate the asymmetric time-varying constraints. Finally, numerical simulations are presented to verify the proposed adaptive control scheme.  相似文献   

15.
This paper studies the finite-time guaranteed cost control problem for switched nonlinear stochastic systems with parameter uncertainties and time-varying delays. By choosing a model-dependent and delay-dependent Lyapunov-Krasovskii functional, applying the average dwell time approach and the Gronwall inequality, some novel sufficient conditions are derived to ensure that the switched nonlinear stochastic closed-loop system is finite-time stochastically stable and an upper bound is given on the performance index. The obtained nonlinear matrix is transformed into a linear matrix form, and then the feedback controller gains of the switched nonlinear stochastic systems with time-varying delay are obtained. Finally, two simulation examples are designed to verify the effectiveness of the suggested approach.  相似文献   

16.
This paper studies the problems of stability and H∞ model reference tracking performance for a class of asynchronous switched nonlinear systems with uncertain input delay. First, it is assumed switched controller and corresponding piecewise Lyapunov function are unknown but the derivative of piecewise Lyapunov function has a condition; this condition implies that the nominal system (system without input delay and disturbance) is exponentially stable by any switched controller which satisfies this condition. With this assumption, a proper Lyapunov–Krasovskii functional is constructed. By employing this new functional and average dwell time technique, the delay-dependent input-to-state stability criteria are derived under a certain delay bound; in addition, a mechanism which finds the upper bound of input delay is proposed. Finally, a kind of state feedback control law which fulfils condition of aforesaid piecewise Lyapunov function is introduced to guarantee the input-to-state stability and H∞ model reference tracking performance. Simulation examples are presented to demonstrate the efficacy of results.  相似文献   

17.
This paper is concerned with the issue of finite-time boundedness of discrete-time uncertain interval type-2 fuzzy systems with time-varying delay and external disturbances via an observer-based reliable control strategy. According to the system output variable, a full-state observer that shares the same membership functions of the plant is constructed to estimate the unknown system states. In addition, a reliable controller subject to observer states and actuator faults is designed to formulate the closed-loop feedback control system, which does not share the same membership functions of the plant. Then, by constructing an appropriate Lyapunov–Krasovskii functional and using the finite-time stability theory, a new set of delay-dependent sufficient conditions guaranteeing the finite-time boundedness of the addressed system is established in the framework of linear matrix inequalities. Furthermore, the explicit expressions of gain matrices of the state observer and the reliable controller are given in terms of the established sufficient conditions. Finally, simulation results are presented to demonstrate the effectiveness of the obtained theoretical results.  相似文献   

18.
In this paper, the global output feedback tracking control is investigated for a class of switched nonlinear systems with time-varying system fault and deferred prescribed performance. The shifting function is introduced to improve the traditional prescribed performance control technique, remove the constraint condition on the initial value, and make the constraint bounds have more alternative forms. To estimate the unmeasured state variables and compensate the system fault, the switched dynamic gain extended state observer is constructed, which relaxes the traditional Lipschitz conditions on the nonlinear functions. Based on the proposed observer, by constructing the new Lyapunov function and using the backstepping method, the global robust output feedback controller is designed to make the output track the reference signal successfully, and after the adjustment time, the tracking error enters into the prescribed set. The stability of the system is analyzed by the average dwell time method. Finally, simulation results are given to illustrate the effectiveness of the proposed method.  相似文献   

19.
This paper explores the finite-time bounded issue for discrete-time singular time-varying delay system via sliding mode control method. A suitable discrete-time sliding mode control law is constructed to drive the state trajectories onto the specified sliding surface in a given finite time interval. Meanwhile, sufficient conditions for finite-time bounded to the closed-loop delayed system are provided in both reaching phase and sliding motion phase. In addition, the finite-time sliding mode controller gain matrix can be solved by using the linear matrix inequalities approach. Finally, three numerical examples are illustrated to demonstrate the superiority and practicability of presented results.  相似文献   

20.
This paper addresses the event-triggered tracking control design for state-constrained switched nonstrict feedback nonlinear systems. With the help of a time-varying nonlinear shifting function (TVNSF) introduced into the switched nonlinear system, the proposed solution is seen as a unified tool regardless of whether the constraint conditions are state constraints, output constraint, or even no constraint. Also, by allowing the triggering error to vary with the switching signal in time, the negative effects of the mismatch between the individual controller and the subsystem on system performance are trumped. Moreover, by using constructed individual Lyapunov function that depends on the lower bound of the control gain function of individual subsystem, a novel switching signal satisfying the average dwell time (ADT) is provided to ensure the boundedness of all variables in the closed-loop system. Finally, the proposed theory is carried over into a mass-spring-damper system to verify its effectiveness.  相似文献   

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