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In this paper, the stability analysis and H ∞ control problems for a class of continuous-time switched systems with a random switching signal are addressed. The dwell time of the switched systems is characterized with a fixed part and a random part. A new stability criterion, which is equivalent to a necessary and sufficient condition developed previously, is established first, and then it is reformulated in terms of linear matrix inequalities. Based on the stability analysis result, L 2 -gain performance analysis and H ∞ control problems are studied. Several numerical examples are given to illustrate the effectiveness of our results.

In this paper, a novel parameter-memorized Lyapunov function is proposed for stability analysis of discrete-time linear systems with time-varying parametric uncertainties. The parameter-memorized Lyapunov function depends on the uncertain parameters with a memory of a certain interval. It is shown that the previous parameter-dependent Lyapunov function is a special memoryless case of the parameter-memorized Lyapunov function, and as a result, the parameter-memorized Lyapunov function approach leads to less conservative results. Furthermore, if the length of the interval for parameter memory is sufficiently long, a nonconservative stability analysis result can be achieved. Numerical examples are provided to evaluate the obtained theoretical results.

This paper deals with the problems of stability analysis and L 1 -gain characterization for continuous-time switched systems consisting of positive subsystems. With the aid of a discretized copositive Lyapunov function, a sufficient condition ensuring the asymptotic stability of continuous-time switched positive systems under dwell-time constraint is obtained, which can be checked via linear programming. Furthermore, the conservatism of the proposed approach is studied and the result with least conservatism in the framework of discretized copositive Lyapunov function is obtained. The result is then extended to L 1 -gain characterization for switched positive systems. With a prescribed dwell time, an unweighted L 1 -gain can be computed via solving a linear programming problem. A numerical example and a practical traffic example are given to illustrate our results.

In this paper, an elementary time unit (ETU) method is proposed to study the problem of estimating the admissible delay in the identification of the active mode in the analysis and design of switched systems. The activation interval of a subsystem is considered to consist of a finite-time number of segments called ETUs, by which a novel class of time-scheduled Lyapunov function is used to estimate the admissible delay in mode identification for switched systems. Further, the ETU method is applied for switching-delay tolerant control problem, and a class of time-scheduled state feedback controllers are designed to achieve the exponentially stability. Several numerical examples are presented to validate the theoretic findings.

In this note, a study on the equivalence of two stability criteria for continuous-time switched linear systems with dwell time constraint is presented. It is demonstrated that, for any dwell time satisfying the conditions in stability criterion proposed in Geromel and Colaneri (2006), the conditions in stability criterion of Allerhand and Shaked (2011) also hold as long as the number of decision variables and related LMIs is sufficiently large, which implies the two stability criteria are intrinsically equivalent. The equivalence is obtained by showing that two criteria can be derived from each other with a sufficiently large number of decision variables and LMIs. A numerical example is proposed to illustrate the theoretical results, and an extension to uncertain case is briefly presented.

Stabilization of switched systems composed fully of unstable subsystems is one of the most challenging problems in the field of switched systems. In this brief paper, a sufficient condition ensuring the asymptotic stability of switched continuous-time systems with all modes unstable is proposed. The main idea is to exploit the stabilization property of switching behaviors to compensate the state divergence made by unstable modes. Then, by using a discretized Lyapunov function approach, a computable sufficient condition for switched linear systems is proposed in the framework of dwell time; it is shown that the time intervals between two successive switching instants are required to be confined by a pair of upper and lower bounds to guarantee the asymptotic stability. Based on derived results, an algorithm is proposed to compute the stability region of admissible dwell time. A numerical example is proposed to illustrate our approach.