On Stability of a Class of Switched Nonlinear Systems Subject to Random Disturbances

This paper addresses the stability problem for a class of switched nonlinear systems subject to random disturbances whose τ-order moments (τ > 1) are finite. First, some general conditions are given to guarantee the existence and uniqueness of solutions to random switched systems. Next, these results are used to deduce the criteria of noise-to-state stability under probabilistic switching signal. Then, the average dwell-time approach is adopted to study the noise-to-state stability, the eλt-weighted (integral) noise-to-state stability and the global asymptotic stability of random switched systems. All the criteria on global existence and stability of solutions are developed by virtue of multiple Lyapunov functions. Finally, two numerical examples are given to demonstrate the validity of the theoretical results.