Premium
Finite‐time stability of switched positive linear systems
Author(s) -
Chen Guopei,
Yang Ying
Publication year - 2012
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.2870
Subject(s) - lyapunov function , dwell time , linear system , positive systems , control theory (sociology) , mathematics , stability (learning theory) , stability theory , function (biology) , state (computer science) , computer science , nonlinear system , algorithm , mathematical analysis , control (management) , medicine , clinical psychology , physics , quantum mechanics , machine learning , evolutionary biology , biology , artificial intelligence
SUMMARY This brief paper addresses the finite‐time stability problem of switched positive linear systems. First, the concept of finite‐time stability is extended to positive linear systems and switched positive linear systems. Then, by using the state transition matrix of the system and copositive Lyapunov function, we present a necessary and sufficient condition and a sufficient condition for finite‐time stability of positive linear systems. Furthermore, two sufficient conditions for finite‐time stability of switched positive linear systems are given by using the common copositive Lyapunov function and multiple copositive Lyapunov functions, a class of switching signals with average dwell time is designed to stabilize the system, and a computational method for vector functions used to construct the Lyapunov function of systems is proposed. Finally, a concrete application is provided to demonstrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.