Improved delay-dependent stability criteria for stochastic systems with time delay and uncertainties

This paper is concerned with the robust asymptotical stability in mean square for stochastic systems with time delay and two kinds of uncertainties. Firstly, a Lyapunov-Krasoskii functional of more complete form is constructed. Then, in order to establish the robust stability criteria for stochastic time-delay systems with two kinds of uncertainties in the same frame, a new variable is introduced to replace the uncertainties and slack matrices are used. Based on Itô calculus rules, the action of the infinitesimal generator of Itô diffusion on the constructed functional is computed and the novel delay-dependent sufficient conditions is obtained in terms of LMIs. Numerical examples are given to illustrate that the results presented in this paper are effective and less conservative than the existing ones.