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Stability and stabilization of continuous‐time switched systems: A multiple discontinuous convex Lyapunov function approach
Author(s) -
Wang Ruihua,
Hou Linlin,
Zong Guangdeng,
Fei Shumin,
Yang Dong
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.4449
Subject(s) - dwell time , control theory (sociology) , lyapunov function , mathematics , stability (learning theory) , constructive , regular polygon , function (biology) , convex combination , set (abstract data type) , convex optimization , computer science , control (management) , nonlinear system , process (computing) , medicine , clinical psychology , physics , geometry , quantum mechanics , artificial intelligence , machine learning , evolutionary biology , biology , operating system , programming language
Summary In this paper, the problems of stability and stabilization are considered for a class of switched linear systems with slow switching and fast switching. A multiple convex Lyapunov function and a multiple discontinuous convex Lyapunov function are first introduced, under which the extended stability and stabilization results are derived with a mode‐dependent average dwell time switching strategy, where slow switching and fast switching are exerted on stable and unstable subsystems, respectively. These two types of Lyapunov functions are established in a constructive manner by virtue of a set of time‐varying functions. By using our proposed approaches, larger stability regions of system parameters are identified, and tighter bounds can be obtained for the mode‐dependent average dwell time. New mode‐dependent and time‐varying controllers are constructed for a class of switched control systems with stabilizable and unstabilizable subsystems as well. All the stability and stabilization conditions can be given in terms of strict linear matrix inequalities (LMIs), which can be checked easily by using recently developed algorithms in solving LMIs. Finally, two numerical examples are provided to show the effectiveness of the obtained results compared with the existing results.