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Strongly absolute stability of Lur'e descriptor systems: Popov‐type criteria
Author(s) -
Yang Chunyu,
Zhang Qingling,
Zhou Linna
Publication year - 2008
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.1350
Subject(s) - stability (learning theory) , mathematics , type (biology) , lyapunov function , property (philosophy) , derivative (finance) , absolute (philosophy) , function (biology) , control theory (sociology) , computer science , nonlinear system , control (management) , physics , artificial intelligence , economics , epistemology , ecology , philosophy , quantum mechanics , machine learning , evolutionary biology , financial economics , biology
In this paper, we consider the strongly absolute stability problem of Lur'e descriptor systems (LDSs). First, we define a generalized Lur'e Lyapunov function (GLLF) and show that the negative‐definite property of the derivative of the GLLF guarantees strongly absolute stability of LDSs. As a result, the existing Popov‐type criteria are reduced to sufficient conditions for the existence of the GLLF. Then, we propose a necessary and sufficient condition for the existence of the GLLF to guarantee the strongly absolute stability of LDSs. This criterion is shown to be less conservative than the existing ones. Finally, we discuss the computational issues and present two numerical examples to illustrate the effectiveness of the obtained results. Copyright © 2008 John Wiley & Sons, Ltd.