Stability analysis and control for switched stochastic delayed systems

This paper investigates almost sure exponential stability and feedback stabilization for switched time-delay systems with nonlinear stochastic perturbations. The main contributions of this paper are threefold: (i) based on the non-convolution type multiple Lyapunov functionals and the mathematical induction approach, a mean-square exponential stability condition for nonlinear stochastic switched systems is first established, such that the obtained average dwell time does not rely on any given decay rate; (ii) by using the method developed in part (i) and the stochastic analysis techniques and limit methods in probability, an almost sure exponential stability criterion for switched delayed systems with nonlinear stochastic uncertainties is presented, and then a state feedback controller for the systems under consideration is designed; and (iii) when certain assumptions are made on the nonlinear stochastic perturbations, the results in this paper are further improved by relaxing some conditions. The effectiveness of the proposed method is demonstrated by three illustrative examples.