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Robust quasi‐time‐dependent control for switched time‐delay systems with performance guarantee
Author(s) -
Zhang Xu,
Wang Jianfeng,
Wu Meixi,
Xu Zhe
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.2640
Subject(s) - dwell time , control theory (sociology) , upper and lower bounds , exponential stability , stability (learning theory) , controller (irrigation) , quadratic equation , mathematics , state (computer science) , computer science , mathematical optimization , control (management) , nonlinear system , physics , geometry , algorithm , quantum mechanics , artificial intelligence , machine learning , agronomy , biology , medicine , clinical psychology , mathematical analysis
Summary In this paper, guaranteed cost control for a class of switched linear systems subject to time delays is investigated, where a nonweighted quadratic performance index is considered. In particular, a novel quasi‐time‐dependent Lyapunov‐Krasovskii function based on a time‐varying positive definite matrix is proposed that is decreasing during the switching intervals and at the switching instants. By exploiting this interesting property, a family of stability condition based on mode‐dependent dwell time is developed to guarantee asymptotic stability of the considered switched linear system. Moreover, design condition for the quasi‐time‐dependent state feedback controller is formulated by extending the stability conditions, guaranteeing asymptotic stability of the closed‐loop system and an initial‐condition‐dependent upper bound of the performance index. A computationally traceable optimization problem is presented to minimize the proposed upper bound as well. A numerical example is considered to show the effectiveness of the proposed control method.