Delay-dependent stability of stochastic systems with time-varying delays

The idea of free-weighting matrices was extended to a class of stochastic systems with time-varying delays, and the delay-dependent stability of the stochastic systems was studied. By establishing a new Lyapunov function and introducing appropriate free-weighting matrices, a sufficient delay-dependent condition was proposed for the asymptotic stability of such a system. The result was in the form of linear matrix inequalities completely and model transformation was unnecessary. Two examples were given to illustrate the effectiveness of the proposed method.