Exponential Stability of Nonlinear Stochastic Systems with Time-delay

This note studies the exponential stability of nonlinear stochastic systems with time delay. Firstly, a more general Lyapunov-Krasovskii functional is constructed, and based on Ito calculus rules for stochastic systems, a novel delay-dependent sufficient condition for exponential stability in mean square is derived in terms of linear matrix inequalities, and it is proved in theory that the obtained stability condition is less conservative. Then, the proposed method is extended to nonlinear time-delay systems and retarded time-delay systems and the corresponding stability criteria are obtained. Finally, numerical examples are given to illustrate that the obtained results in this paper are less conservative than some existing ones.