Almost surely attractive sets of discrete-time Markov jump systems with stochastic disturbances via impulsive control

In this study, the problem on the globally almost surely attractive sets is addressed for a class of discrete-time Markov jump systems with stochastic disturbances via impulsive control. Based on the Lyapunov function methods and the Markov's inequality, the authors derive some sufficient conditions guaranteeing the existence of the global almost surely attractive sets of the considered systems. Meanwhile, the estimation of the attractive sets is also given out. It is shown that the unbounded discrete-time Markov jump stochastic system without attractive sets can turn into the bounded one with attractive sets via proper impulsive control strategies. An example is also presented to illustrate the main results.