Stochastic stability of nonlinear positive systems with random switching signals. (November 2020) - Zhao, Ping; Zhao, Yan; Song, Xinmin
Abstract: In this paper, we are concerned with stochastic stability of nonlinear positive systems with random switching signals. The random switching signals are triggered by a stochastic process which is independent of the state of the system. Our results provide sufficient conditions on global asymptotic stability in stochastic sense for nonlinear positive systems when individual subsystems are stable and a certain slow switching condition holds. This slow switching condition takes the form of an asymptotic upper bound on the non-homogeneous probability mass function of the number of switches that occur between the initial and current time instants. Due to the "non-homogeneousness", the non-homogeneous Poisson process and semi-Markov process are included to generate the switching signals. Simulation example verifies the validity of our results.