On stability of switched time-delay systems subject to nonlinear stochastic perturbations

In this paper we investigate the problem of exponential stability for a class of switched time-delay systems subject to nonlinear stochastic perturbations. The multiple Lyapunov functionals approach is utilized to derive new mean-square exponential and almost sure exponential stability conditions for the switched time-delay systems under consideration. In particular, the generalized Finsler Lemma (GFL), which is applicable to time-delay systems in the stochastic framework, plays a central role in the derivation so that neither model transformations nor free-weighting matrices are required. Numerical examples are included to illustrate the performance of the proposed method.