Stochastic stability and stabilization of positive Markov jump linear impulsive systems with time delay

Abstract

This paper investigates the stochastic stability and stabilization of positive Markov jump linear impulsive systems (PMJLIS) with time delay. First, by choosing appropriate co-positive Lyapunov–Krasovskii functional and using the impulsive average dwell-time method, a stochastic stability criterion is provided for PMJLIS with time delay. Based on this criterion, for PMJLIS with time delay, the stabilization conditions are given using state feedback and impulse feedback, respectively. According to this criteria, the stochastic stability of the systems can be judged and the controllers can be designed only from some relations of the coefficient matrices, Markov jump parameters and delay. To illustrate the main results, a simulation example is provided at the end with a state-feedback controller and an impulsive controller is designed, respectively, which makes the corresponding closed-loop systems be positive, globally asymptotically stable in probability and globally asymptotically stable in mean.