Delay-dependent exponential stability criteria for stochastic systems with polytopic-type uncertainties

Abstract

This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities (LMIs), and some new delay-dependent criteria are obtained. These criteria include the delay-independent/ratedependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.