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Finite‐time stability of fractional order impulsive switched systems
Author(s) -
Yang Ying,
Chen Guopei
Publication year - 2014
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.3202
Subject(s) - mathematics , lemma (botany) , lyapunov function , stability (learning theory) , order (exchange) , dwell time , fractional calculus , function (biology) , control theory (sociology) , nonlinear system , fractional order system , computer science , medicine , ecology , clinical psychology , physics , poaceae , control (management) , finance , quantum mechanics , machine learning , evolutionary biology , artificial intelligence , economics , biology
Summary This paper considers the finite‐time stability of fractional order impulsive switched systems. First, by using the fractional order Lyapunov function, Mittag–Leffler function, and Gronwall–Bellman lemma, two sufficient conditions are given to verify the finite‐time stability of fractional order nonlinear systems. Then, the concept of finite‐time stability is extended to fractional order impulsive switched systems. A sufficient condition is given to verify the finite‐time stability of fractional order impulsive switched systems by combining the method of average dwell time with fractional order Lyapunov function. Finally, two numerical examples are provided to illustrate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.