Positive Effect of Switching on Input-to-State Stability of Nonlinear Systems

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.