New absolute stability criteria for time‐delay Lur'e systems with sector‐bounded nonlinearity

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.

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