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New absolute stability criteria for time‐delay Lur'e systems with sector‐bounded nonlinearity
Author(s) -
Liu Xian,
Wang Jinzhi,
Duan Zhisheng,
Huang Lin
Publication year - 2010
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.1460
Subject(s) - circle criterion , mathematics , bounded function , control theory (sociology) , stability (learning theory) , nonlinear system , convex optimization , domain (mathematical analysis) , time domain , frequency domain , set (abstract data type) , regular polygon , stability criterion , upper and lower bounds , exponential stability , computer science , mathematical analysis , control (management) , statistics , discrete time and continuous time , physics , geometry , quantum mechanics , artificial intelligence , computer vision , machine learning , programming language
This paper is concerned with the problem of absolute stability of time‐delay Lur'e systems with sector‐bounded nonlinearity. Several novel criteria are presented by using a Lur'e–Postnikov function. For a general Lur'e system with known time delay, the absolute stability of it is analyzed by solving a set of linear matrix inequalities (LMIs). The maximum upper bound of the allowable time delay for a general Lur'e system is derived by solving a convex optimization problem. The feasibility of the LMIs implies some frequency‐domain interpretations which are similar to the frequency‐domain inequalities in the circle criterion and the Popov criterion. Copyright © 2009 John Wiley & Sons, Ltd.