Exponential estimates and H∞ control for singular Markovian jump systems with interval time-varying delay

Abstract

This paper is concerned with exponential estimates and H∞ control for a class of singular Markovian jump systems with interval time-varying delay. By constructing an appropriate Lyapunov-Krasovskii functional and using some algebraic techniques, a sufficient condition, which does not only guarantee the regularity, absence of impulses, and mean square exponential stability but also gives the estimates of decay rate and decay coefficient, is derived in terms of linear matrix inequalities (LMIs). A bounded real lemma is also developed. Based on these, a state-feedback controller which makes the closed-loop system stochastically exponentially admissible with a guaranteed H∞ noise-attenuation performance and a prescribed lower bound of the decay rate is designed by employing the LMI technique. Numerical examples are provided to illustrate the effectiveness of the proposed design methods.