Stability Analysis for Nonlinear Switched Positive Systems With Markov Chain Impulses

The aim of this paper is to investigate the issue of stochastically exponential stability in positive nonlinear impulsive switching systems that involve random impulses. The random impulses means that the randomness of impulsive densities and the occurrence of the impulses is a Markov chain. The occurrence instants of impulses also satisfy average impulsive intervals. This research employs the multiple max-separable Lyapunov function method to investigate two cases: asynchronous/synchronous switching and impulses. Then the stochastic exponential stability conditions are given. Finally, to demonstrate the validity of the theoretical results, two illustrative examples are provided.