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

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