Delay-dependent exponential stability of uncertain stochastic systems with time-varying delay and nonlinearities

This paper deals with the problem of delay-dependent exponential stability in the mean square for a class of uncertain stochastic systems with time-varying delay and nonlinearities. By using Lyapunov-Krosovskii functional method combined with linear matrix inequalities (LMIs) techniques, some new delay-dependent stability criteria in terms of LMIs are derived by introducing some free weighting matrices which can be selected properly to lead to less conservative results. Maximum allowable delay bound (MADB) to guarantee the exponential stability of the systems can be obtained effectively by solving a set of LMIs. Numerical example and simulation are given to show that the proposed methods are effective and are much less conservative than some existing results.