Stability of uncertain stochastic systems with time-varying delays based on parameter-dependent Lyapunov functional

The robust stability analysis for a class of linear stochastic systems with polytopic-type uncertainties and time-varying delays is considered in this paper. By introducing some slack matrices, and finding the relation between the terms in the Leibniz-Newton formula, a sufficient delay-dependent condition is proposed for the robust asymptotic stability of such a system by applying the parameter-dependent Lyapunov functional approach. In contrast to the traditional method of using model transformation to derive the delay-dependent condition, this new stability condition is less conservative. The resultant stability condition is in the form of linear matrix inequalities (LMIs), which can be solved via efficient interior-point algorithms. A numerical example is also presented to illustrate the less conservative properly of the proposed stability condition.