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Reachable set estimation for discrete‐time switched system with application to time‐delay system
Author(s) -
Fei Zhongyang,
Guan Chaoxu,
Shi Peng
Publication year - 2018
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.4028
Subject(s) - dwell time , control theory (sociology) , bounding overwatch , discrete time and continuous time , ellipsoid , bounded function , set (abstract data type) , controller (irrigation) , exponential stability , computer science , stability (learning theory) , upper and lower bounds , mathematics , control (management) , nonlinear system , medicine , clinical psychology , mathematical analysis , statistics , physics , astronomy , artificial intelligence , quantum mechanics , machine learning , agronomy , biology , programming language
Summary This paper addresses the problem of reachable set estimation and synthesis for a class of discrete‐time switched linear systems with time delay and bounded peak disturbance. Combined with the feature of mode‐dependent average dwell time switching, a new algorithm is developed to estimate the reachable set of switched system, which is both quasi‐time‐dependent and mode‐dependent. Then, the proposed method is applied to time‐delay system and a sufficient condition is presented to guarantee the asymptotic stability and estimate the bounding ellipsoid. Furthermore, the quasi‐time‐dependent controller is designed to stabilize the system and restrict the closed‐loop system states to an ellipsoidal bound. Examples are presented to illustrate the effectiveness and advantages of the obtained theorems.