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Lur'e Lyapunov functions and absolute stability criteria for Lur'e systems with multiple nonlinearities
Author(s) -
Yang Chunyu,
Zhang Qingling,
Zhou Linna
Publication year - 2007
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.1155
Subject(s) - lyapunov function , mathematics , stability (learning theory) , control theory (sociology) , function (biology) , computer science , nonlinear system , control (management) , artificial intelligence , physics , quantum mechanics , machine learning , evolutionary biology , biology
In this paper, the absolute stability problem of Lur'e systems with multiple nonlinearities is investigated. Popov‐type absolute stability criteria are surveyed and classified by distinguishing the Lur'e Lyapunov function upon which the criteria are based. A modified Lur'e Lyapunov function is presented. Some necessary and sufficient conditions for the existence of the Lyapynov function to guarantee the absolute stability of Lur'e systems are derived. By these conditions, LMI‐based stability criteria are presented. The obtained criteria are expected to be less conservative than the existing ones. Finally, numerical examples are given to illustrate the advantages and effectiveness of our results. Copyright © 2006 John Wiley & Sons, Ltd.