Improved stability criteria for uncertain stochastic systems with time-delay

This paper is concerned with the asymptotical stability in mean square for uncertain stochastic time-delay system. Firstly, a new variable is defined, by which some slack matrices are introduced to reduce the conservatism of the result. Then, a proper Lyapunov-Krasovskii functional is constructed and its infinitesimal operator is calculated by Itô calculus rules and the statistic properties of the Brownian motion, and as a result the delay-dependent stability criteria are obtained via an LMI approach. Finally, numerical examples are given to illustrate the significant improvement on the conservativeness of the delay bound over some existing results.