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Asymptotic stability and stabilization of discrete‐time switched systems with time‐varying delay
Author(s) -
Charqi Mohammed,
Tissir El Houssaine,
Boukili Bensalem
Publication year - 2020
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2684
Subject(s) - control theory (sociology) , stability (learning theory) , exponential stability , discrete time and continuous time , controller (irrigation) , class (philosophy) , mathematics , state (computer science) , relaxation (psychology) , full state feedback , computer science , control (management) , algorithm , nonlinear system , psychology , social psychology , statistics , physics , quantum mechanics , machine learning , artificial intelligence , agronomy , biology
Summary This article deals with the problems of stability and stabilization for a class of discrete‐time switched systems with time‐varying delay under arbitrary switching signal. First, sufficient conditions guaranteeing the asymptotic stability of the unforced system are developed, by using the switched Lyapunov‐Krasovskii functional method. Then, based on the obtained results, a state feedback controller is designed in order to ensure the asymptotic stability of the closed‐loop system. Furthermore, slack variables are introduced for more relaxation. The proposed approach is proved to have some less conservative results than some existing works. Finally, numerical examples are provided to illustrate the effectiveness and the merit of the proposed method and to compare the obtained results with some previous works in the literature.