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Stability and stabilization of nonlinear discrete‐time stochastic systems
Author(s) -
Jiang Xiushan,
Tian Senping,
Zhang Tianliang,
Zhang Weihai
Publication year - 2019
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4733
Subject(s) - discrete time and continuous time , exponential stability , nonlinear system , mathematics , stability (learning theory) , discrete time stochastic process , class (philosophy) , control theory (sociology) , linear matrix inequality , mathematical optimization , control (management) , computer science , continuous time stochastic process , stochastic differential equation , statistics , physics , quantum mechanics , machine learning , artificial intelligence
Summary This paper mainly studies the locally/globally asymptotic stability and stabilization in probability for nonlinear discrete‐time stochastic systems. Firstly, for more general stochastic difference systems, two very useful results on locally and globally asymptotic stability in probability are obtained, which can be viewed as the discrete versions of continuous‐time Itô systems. Then, for a class of quasi‐linear discrete‐time stochastic control systems, both state‐ and output‐feedback asymptotic stabilization are studied, for which, sufficient conditions are presented in terms of linear matrix inequalities. Two simulation examples are given to illustrate the effectiveness of our main results.