Robust exponential stability conditions for retarded systems with Lipschitz nonlinear stochastic perturbations

This paper investigates robust mean-square exponential stability of a class of uncertain stochastic state-delayed systems with Lipschitz nonlinear stochastic perturbation. Based on Lyapunov-Krasovskii functional (LKF) method and free-weighting matrix technique, some new delay-dependent stability conditions are established in terms of linear matrix inequalities (LMIs). In order to reduce the conservatism, (1) the delay is divided into several segments, i.e. the delay decomposition method is applied; (2) cross terms estimation is avoided; (3) some information of the cross terms relationships which has not been involved in Reference (IET Control Theory Appl. 2008; 2(11):966-973) is considered. Moreover, from the mathematical point of view, the results obtained by free-weighting matrix technique can be equivalently re-formulated by simpler ones without involving any additional free matrix variables. The effectiveness of the method is demonstrated by numerical examples.