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Exponential Stabilization of Switched Discrete‐Time Systems with All Unstable Modes
Author(s) -
Li Jiao,
Ma Zixiao,
Fu Jun
Publication year - 2018
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1651
Subject(s) - dwell time , lyapunov function , control theory (sociology) , exponential stability , mathematics , discrete time and continuous time , exponential function , stability (learning theory) , function (biology) , upper and lower bounds , exponential growth , interval (graph theory) , class (philosophy) , computer science , mathematical analysis , control (management) , nonlinear system , physics , combinatorics , medicine , clinical psychology , statistics , quantum mechanics , artificial intelligence , machine learning , evolutionary biology , biology
This paper studies the exponential stabilization of switched discrete‐time systems whose subsystems are unstable. A new sufficient condition for the exponential stability of the class of systems is proposed. The result obtained is based on the determination of a lower bound of the maximum dwell time by virtue of the multiple Lyapunov functions method. The key feature is that the given stability condition does not need the value of the Lyapunov function to uniformly decrease at every switching instant. An example is provided to illustrate the effectiveness of the proposed result.