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The stability and H ∞ performance analysis of a class of impulsive differential systems are addressed by using a two-point boundary value problem method. For convenience of computation, a sufficient and necessary condition for the existence of a solution to the two-point boundary value problem is expressed using a set of linear matrix inequalities. As an application example, we apply the suggested method to deal with the sampled-data H ∞ filtering problem. A numerical example of a mass–spring system is used to verify the effectiveness of the theoretical result. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of mixed H∞ and passive control for flexible spacecrafts subject to nonuniform sampling and time-varying delay in the input channel. An impulsive observer-based controller is introduced and the resulting closed-loop system is a hybrid system consisting of a continuous time-delay subsystem and an impulsive differential subsystem. As a first result, we derive a generalized bounded real lemma (GBRL), that is, a generalized H∞ performance criterion, for the impulsive differential subsystem by constructing a time-varying Lyapunov functional. Then, on the basis of this GBRL and utilizing the Lyapunov–Krasovskii approach, a sufficient condition is derived to asymptotically stabilize the closed-loop system and simultaneously guarantee a prescribed mixed H∞ and passivity performance index. A design method is proposed for the desired controller, which can be readily constructed by solving a convex optimization problem with linear matrix inequalities (LMIs) constraints. Finally, numerical experiments are provided to support the theoretical results, and comparisons with former approaches are also discussed. [ABSTRACT FROM AUTHOR]