Baowei Wu

H∞ control of singular time-delay systems via discretized Lyapunov functional

Abstract This paper addresses the problem of robust H ∞ control for uncertain continuous time singular systems with state delays. A new singular-type complete quadratic Lyapunov–Krasovskii functional (LKF) is introduced, which combines with the discretization LKF method to synthesis problems. An improved bounded real lemma (BRL) is presented to ensure the system to be regular, impulse free and stable with H ∞ performance condition. Based on the BRL, a memoryless state feedback controller is designed via linear matrix inequalities (LMIs), which greatly reduces the disturbance attenuation level. Numerical examples are given to illustrate improvements over some existing results.

On parameterized Lyapunov–Krasovskii functional techniques for investigating singular time-delay systems

Abstract The problem of robust stability of a singular time-delay system is investigated. A novel Lyapunov–Krasovskii functional (LKF) is introduced which is a singular-type complete quadratic Lyapunov–Krasovskii functional with polynomial parameters. Stability conditions are derived in the form of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and lower conservatism of the new proposed stability criterion.

Asynchronously finite-time control of discrete impulsive switched positive time-delay systems

Abstract The finite-time control for a class of discrete impulsive switched positive time-delay systems under asynchronous switching is discussed in this paper. First, by choosing a Lyapunov–Krasovskii functional, some sufficient conditions for the existence of a family of asynchronously switched controllers are derived such that the resulting closed-loop system is finite-time stable based on the mode-dependent average dwell time approach. Second, the specific form of desired controller gains is given. Moreover, all the obtained results are formulated in terms of algebraic matrix inequalities which can be solved by virtue of LP toolbox. Finally, a numerical example is exploited to show that the obtained results are effective.

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.

Stability and L2-gain analysis of switched input delay systems with unstable modes under asynchronous switching ☆

We consider the stability and L2-gain analysis problem for a class of switched linear systems. We study the effects of the presences of input delay and switched delay in the feedback channels of the switched linear systems with an external disturbance. By contrast with the most of the contributions available in literatures, we do not require that all the modes of the switched system are stable when input delay appears in the feedback input. By reaching a compromise among the matched-stable period, the matched-unstable period, and the unmatched period and permitting the increasing of the multiple Lyapunov functionals on all the switching times, the solvable conditions of exponential stability and weighted L2-gain are developed for the switched system under mode-dependent average dwell time scheme (MDADT). Finally, numerical examples are given to illustrate the effectiveness of the proposed theory.

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 stability of fractional order linear systems with 0 < α < 1

The input–output finite time stability (IO-FTS) for a class of fractional order linear time-invariant systems with a fractional commensurate order 0 < α < 1 is addressed in this paper. In order to give the stability property, we first provide a new property for Caputo fractional derivatives of the Lyapunov function, which plays an important role in the main results. Then, the concepts of the IO-FTS for fractional order normal systems and fractional order singular systems are introduced, and some sufficient conditions are established to guarantee the IO-FTS for fractional order normal systems and fractional order singular systems, respectively. Finally, the state feedback controllers are designed to maintain the IO-FTS of the resultant fractional order closed-loop systems. Two numerical examples are provided to illustrate the effectiveness of the proposed results.

Delay-Dependent Criteria for Robust Stability of Singularly Perturbed Systems with Delays

This paper considers the problem of delay-dependent robust stability for singularly perturbed systems with state delays. Some new delay-dependent stability criteria are derived by employing appropriate Lyapunov-Krasovskii functional. Since some free weighting matrices are used to express the relationship between the terms in the Leibniz-Newton formula, the new criteria are less conservative than existing ones. Numerical examples illustrate the effectiveness of the new theory.

Stability and L1-gain analysis for positive delay systems with large delay period

In this paper, the problems of stability and L 1 -gain performance analysis for positive delay systems with large delay period are investigated. The maximum allowed delay bound is expanded. Under the limitations of frequency and length rate of the large delay period, the sufficient conditions guaranteeing stability of the considered system are obtained and the weighted L 1 -gain performance analysis is established. Detailed proofs are presented by using co-positive Lyapunov–Krasovskii functional candidates with large delay integral terms and the switching method; where the switching method involves transforming the original system into a positive switched delay system. All the obtained conditions can be solved via linear matrix inequalities. Finally, the validity of the proposed results is illustrated by a numerical example.

On designing state estimators for discrete-time recurrent neural networks with interval-like time-varying delays

Abstract This paper deals with designing state estimators for a class of discrete-time recurrent neural networks with interval-like time-varying delays. Based on a delay bi-decomposition idea, a proper Lyapunov functional is introduced, which takes into account more information on the interval-like time-varying delay and the neuronal activation function. This Lyapunov functional, together with an improved reciprocally convex inequality, is employed to derive a sufficient condition to design suitable Luenberger-type estimators by solutions to linear matrix inequalities. An example is taken to show the effectiveness of the proposed method.