Mode-dependent Average Dwell Time Research Articles

Stability analysis of switched systems with extended average dwell time

The problem of stability for switched systems with extended average dwell time (ADT) is investigated in both the continuous-time and discrete-time cases. By proposing three novel concepts of closed-chain, r-open-chain, and quasi-cyclic switching signals, stability and stabilization conditions of switched systems with ADT or mode-dependent ADT (MDADT) switching are obtained. This paper develops and enriches the existing results on stability under constrained switching, since the existing results based on both ADT and MDADT can be seen as the special cases of ours. On the other hand, the paper provides a solution to the open problem of how to obtain a tighter bound on ADT or MDADT. Finally, some comparisons between the existing results and ours show the superiority of the theoretical findings of this paper.

Stability Analysis for Discrete-Time Switched Nonlinear System Under MDADT Switching

The problem of stability analysis for discrete-time switched nonlinear system is investigated with mode-dependent average dwell time (MDADT) method in this paper. A slow switching strategy is adopted in the discrete-time nonlinear stable subsystems and unstable subsystems are handled by a fast switching strategy. Takagi-Sugeno (T-S) fuzzy model is utilized to approximate the switched nonlinear system. By constructing a multiple discontinuous Lyapunov function approach, the stability condition of switched T-S fuzzy system is built to get tighter bound on MDADT, which shows that our proposed method outperforms the classical one. Finally, through a numerical example, the effectiveness of the presented control approach is illustrated by comparison with result from classical one.

Input-Output Finite-Time Control of Positive Switched Systems with Time-Varying and Distributed Delays

The problem of input-output finite-time control of positive switched systems with time-varying and distributed delays is considered in this paper. Firstly, the definition of input-output finite-time stability is extended to positive switched systems with time-varying and distributed delays, and the proof of the positivity of such systems is also given. Then, by constructing multiple linear copositive Lyapunov functions and using the mode-dependent average dwell time (MDADT) approach, a state feedback controller is designed, and sufficient conditions are derived to guarantee that the corresponding closed-loop system is input-output finite-time stable (IO-FTS). Such conditions can be easily solved by linear programming. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

Finite-time stability of discrete-time switched singular systems with all unstable modes

The finite-time stability (FTS) problem of discrete-time switched singular systems consisting of all unstable modes is investigated in this paper. By means of dynamic decomposition technique, the original singular system is converted to a reduced-order normal discrete-time switched system. Following the idea of getting into each unstable mode, its internal behaviour is analysed in detail. Two approaches, namely, the Lyapunov one and the state transition matrix one, are utilised to design the switching law with mode-dependent average dwell time such that the FTS property is guaranteed. It is shown that each of them has its own advantages. Selecting appropriate one depends on the specific object for study. In addition, the corresponding asymptotic stability criteria can be easily derived as a by-product. Finally, two examples are given to verify the obtained results and illustrate the effectiveness of the proposed strategies.

Finite-time stability of discrete-time switched singular systems with all unstable modes

The finite-time stability (FTS) problem of discrete-time switched singular systems consisting of all unstable modes is investigated in this paper. By means of dynamic decomposition technique, the original singular system is converted to a reduced-order normal discrete-time switched system. Following the idea of getting into each unstable mode, its internal behaviour is analysed in detail. Two approaches, namely, the Lyapunov one and the state transition matrix one, are utilised to design the switching law with mode-dependent average dwell time such that the FTS property is guaranteed. It is shown that each of them has its own advantages. Selecting appropriate one depends on the specific object for study. In addition, the corresponding asymptotic stability criteria can be easily derived as a by-product. Finally, two examples are given to verify the obtained results and illustrate the effectiveness of the proposed strategies.

Guaranteed Cost Finite-Time Control for Positive Switched Linear Systems with Time-Varying Delays

This paper considers the guaranteed cost finite-time control for positive switched linear systems with time-varying delays. The definition of guaranteed cost finite-time boundedness is firstly given. Then, by using the mode-dependent average dwell time approach, a static output feedback law and a state feedback control law are constructed, respectively, and sufficient conditions are obtained to guarantee that the closed-loop system is guaranteed cost finite-time boundedness. Such conditions can be easily solved by linear programming. Finally, an example is given to illustrate the effectiveness of the proposed method.

Stability of switched neural networks with time-varying delays

This paper investigates the globally exponential stability of switched neural networks with time-varying delays. By virtue of mode-dependent average dwell time, some significant criteria of exponential stability are obtained for delayed switched neural networks with only stable subsystems or with both stable subsystems and unstable subsystems. The proposed theoretical results could be utilized not only to verify the globally exponential stability of switched neural networks, but also to design appropriate switching signal to guarantee the globally exponential stabilization. They can explicitly reflect the effect of mode-dependent average dwell time on the stability of switched neural networks. In contrast to the previous results, the proposed criteria are more straightforward and effective in the real-world application. Three numerical examples are introduced to illustrate the effectiveness of the proposed results.

Improved results on exponential stability of discrete-time switched delay systems

In this paper, we study the exponential stability problem of discrete-time switched delay systems. Combining a multiple Lyapunov function method with a mode-dependent average dwell time technique, we develop novel sufficient conditions for exponential stability of the switched delay systems expressed by a set of numerically solvable linear matrix inequalities. Finally, numerical examples are presented to illustrate less conservativeness of the obtained results.

Robust adaptive state estimation for uncertain nonlinear switched systems with unknown inputs

This paper discusses the issue of the continuous state estimation for a class of uncertain nonlinear switched systems under the two cases of both average dwell time and mode-dependent average dwell time. A robust and adaptive switched observer is developed such that the states of an original nonlinear switched system can be asymptotically estimated, where the Lipschitz constant of the nonlinear term may be unknown since the designed adaptation law can adaptively adjust it. Based on the feasible solution of an optimization problem with a linear matrix inequality constraint, the observer gain matrices are obtained and guarantee the existence of a robust switched observer. Meanwhile, the switching signals are designed such that the observer error dynamics is globally uniformly exponentially stable, and the sufficient conditions of the existence of a robust sliding-mode switched observer are derived. Finally, the effectiveness of the proposed approaches is illustrated by a numerical example and switched Rössler chaotic dynamics.

Finite-Time Stability of Discrete Switched Singular Positive Systems

The finite-time stability problem of discrete switched singular positive systems (DSSPSs) is investigated in this paper. First, the concept of finite-time stability for DSSPSs is proposed, and a necessary and sufficient condition of finite-time stability for DSSPSs under arbitrary switching is obtained. Second, based on the mode-dependent average dwell time approach, by constructing the quasi-linear Lyapunov function, a sufficient stability criterion of finite-time stability for DSSPSs is derived in terms of a set of linear matrix inequalities. Finally, a numerical example is given to show the effectiveness of the proposed techniques.

Input–output finite-time stabilization of a class of nonlinear hybrid systems based on FSM with MDADT

This thesis investigates the problem of input–output finite-time stabilization for a class of nonlinear impulsive hybrid systems based on finite state machine (FSM). First, the concept of input–output finite-time stability (IO-FTS) is extended for such hybrid systems, then, the stability analysis is given by combining the multiple Lyapunov functions (MLFs) method and mode-dependent average dwell time (MDADT) technique, the corresponding sufficient conditions are derived and proved. Furthermore, a state feedback controller is designed to stabilize the hybrid systems. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed controller.

Stability analysis of switched cellular neural networks: A mode-dependent average dwell time approach

This paper addresses the exponential stability of switched cellular neural networks by using the mode-dependent average dwell time (MDADT) approach. This method is quite different from the traditional average dwell time (ADT) method in permitting each subsystem to have its own average dwell time. Detailed investigations have been carried out for two cases. One is that all subsystems are stable and the other is that stable subsystems coexist with unstable subsystems. By employing Lyapunov functionals, linear matrix inequalities (LMIs), Jessen-type inequality, Wirtinger-based inequality, reciprocally convex approach, we derived some novel and less conservative conditions on exponential stability of the networks. Comparing to ADT, the proposed MDADT show that the minimal dwell time of each subsystem is smaller and the switched system stabilizes faster. The obtained results extend and improve some existing ones. Moreover, the validness and effectiveness of these results are demonstrated through numerical simulations.

New stabilization results for discrete-time positive switched systems with forward mode-dependent average dwell time

The stability and stabilization of discrete-time linear positive switched systems are discussed in this paper. First, based on the concept of the forward mode-dependent average dwell time, a stability result for discrete-time linear positive switched systems is obtained by utilizing the multiple linear copositive Lyapunov functions. Then, by introducing multiple-sample Lyapunov-like functions variation, a new exponential stability result is derived. Finally, the conditions for the existence of mode-dependent stabilizing state feedback controllers are investigated, and two illustrative examples are given to show the correctness of the theoretical results obtained.

Stabilization of Discrete‐time Switched Systems with State Constraints Based on Mode‐Dependent Average Dwell Time

AbstractThis paper considers the stabilization problem for a class of switched systems with state constraints based on mode‐dependent average dwell time (MDADT) in discrete‐time context. An improved average dwell time method is proposed, which is less conservative than the common average dwell time method. The sufficient conditions and stabilizing state feedback controllers for stabilization of discrete‐time switched systems with state constraints under MDADT switching are derived. Finally, the simulation results show that the approach designed by this paper is effective.

New Stability and Stabilization Conditions of Switched Systems with Mode-Dependent Average Dwell Time

In this paper, the problems of stability and stabilization for switched systems with mode-dependent average dwell time (MDADT) switching are revisited and discussed in both continuous-time and disc...

Global exponential stability for switched memristive neural networks with time-varying delays

This paper considers the problem of exponential stability for switched memristive neural networks (MNNs) with time-varying delays. Different from most of the existing papers, we model a memristor as a continuous system, and view switched MNNs as switched neural networks with uncertain time-varying parameters. Based on average dwell time technique, mode-dependent average dwell time technique and multiple Lyapunov–Krasovskii functional approach, two conditions are derived to design the switching signal and guarantee the exponential stability of the considered neural networks, which are delay-dependent and formulated by linear matrix inequalities (LMIs). Finally, the effectiveness of the theoretical results is demonstrated by two numerical examples.

Mode‐dependent event‐triggered control of networked switching Takagi–Sugeno fuzzy systems

This study presents a novel mode-dependent event-triggering (MDET) scheme for networked switching Takagi–Sugeno fuzzy systems. Firstly, a new delay system model for the stability analysis is proposed by considering network-induced delay. Then, based on this model and mode-dependent average dwell time method, sufficient conditions are obtained to guarantee the exponential stability. Criteria for co-designing the event generator parameters and the controller gain matrices are given. Finally, numerical examples are provided to show that the MDET scheme proposed in this study is less conservative than some existing event-triggering schemes.

Control of Switched Nonlinear Systems via T–S Fuzzy Modeling

This paper is concerned with the control problem for a class of switched nonlinear systems possibly composed of all unstable modes by using time-controlled switching signals. To tackle the problem, a new mode-dependent average dwell time (MDADT) switching property is proposed, which is different from the existing one in the literature. Then, the stabilization condition under such MDADT switching signals is established for the switched nonlinear systems with possibly all unstable subsystems. By proposing a class of time-scheduled multiple quadratic Lyapunov function and applying T–S fuzzy models to represent the underlying nonlinear subsystems, numerically easily verified stabilization conditions are further derived in the form of linear matrix inequalities. A numerical example is finally provided to illustrate the effectiveness of the obtained theoretical results.

Reliable guaranteed‐cost control of delta operator switched systems with actuator faults: mode‐dependent average dwell‐time approach

This study deals with the reliable guaranteed-cost control problem for a class of delta operator switched linear systems, in terms of mode-dependent average dwell-time (MDADT) approach. Firstly, based on MDADT approach, asymptotical and exponential stabilities of delta operator non-linear switched systems are analysed. Then, the reliable controller and the minimum MDADT are designed to stabilise the considered delta operator linear switched system with actuator faults and to determine an upper bound of the given cost function. A flight control switched system is given to show the validity and potential of the proposed method.

An MDADT-Based Approach forL2-Gain Analysis of Discrete-Time Switched Delay Systems

We study theL2-gain analysis problem for a class of discrete-time switched systems with time-varying delays. A mode-dependent average dwell time (MDADT) approach is applied to analyze theL2-gain performance for these discrete-time switched delay systems. Combining a multiple Lyapunov functional method with the MDADT approach, sufficient conditions expressed in form of a set of feasible linear matrix inequalities (LMIs) are established to guarantee theL2-gain performance. Finally, a numerical example will be provided to demonstrate the validity and usefulness of the obtained results.