Open AccessAlmost surely attractive sets of discrete‐time Markov jump systems with stochastic disturbances via impulsive control
Author(s) -
Xu Liguang,
Dai Zhenlei,
Ge Shuzhi Sam
Publication year - 2019
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2018.5262
Subject(s) - mathematics , discrete time and continuous time , lyapunov function , markov chain , control theory (sociology) , jump , markov process , bounded function , mathematical optimization , jump process , control (management) , computer science , nonlinear system , statistics , physics , quantum mechanics , artificial intelligence , mathematical analysis
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.