Stability analysis for time-varying positive systems with stochastic impulses

This article addresses the stochastically exponential stability and mean stability of positive time-varying systems with stochastic impulses. The term ‘stochastic impulse’ means the randomness of impulsive densities or intensities. More specifically, the impulsive maps are not unique and the impulsive intensities are independent random variables with different distributions. The occurrence instants of impulses are restricted by several different processes, e.g. a mode-dependent average impulsive interval, a Markov chain, a Poisson process and a renewal process. Using a time-varying copositive Lyapunov function and stochastic analysis theory, several stochastic stability conditions are given. Finally, an example with four cases is presented to show the effectiveness of the proposed results.