New stability criteria for semi-Markov jump linear systems with time-varying delays

Abstract

In this paper, the delay-dependent stochastic stability problem of semi-Markov jump linear systems (S-MJLS) with time-varying delays is investigated. By constructing a Lyapunov-Krasovskii functional (LKF) with two delay-product-type terms, a new sufficient condition on stochastic stability of S-MJLSs is derived in terms of linear matrix inequalities (LMIs). Furthermore, the combination use of a slack condition on Lyapunov matrix and the improved Wirtinger's integral inequality reduces the conservatism of the result. Numerical examples are provided to verify the effectiveness and superiority of the presented results.

Keywords

• semi-markov jump linear systems
• time-varying delays
• delay-dependent stability
• wirtinger's integral inequality