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This paper considers the input-to-state stability (ISS) problem of nonlinear switched systems under stochastic switching governed by both transition probability and stochastic dwell time. A novel analysis framework of ISS with respect to switched systems is proposed in the sense of Lyapunov. It is shown that the stochastic switching exhibits a positive effect on the ISS issue, and uniform ISS can be achieved even though all subsystems are non-ISS. In addition, the proposed Lyapunov results are applied to linear switched systems by using the linear matrix inequality method, and a novel dynamic feedback control strategy is designed to realize the input-to-state stabilization. Finally, two examples are presented to show the positive effect of stochastic switching and the capability of the proposed dynamic control strategy.
Xu et al. (Mon,) studied this question.