Less conservative absolute stability criteria using integral quadratic constraints

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Scopus citations


Lur'e systems, that are described by the feedback interconnection of a linear time invariant system and a nonlinear system, form an important class of nonlinear systems arising in many modern applications. A number of absolute stability criteria are available where the stability is guaranteed with the nonlinearity restricted to a pre-specified set. Most of these criteria provide sufficient conditions for absolute stability, thus lessening the conservativeness remains a challenge. A method of reducing conservativeness is to first estimate the part of the nonlinearity that is appropriate from an asymptotic sense followed by the application of a preferred absolute stability criteria to the more restricted nonlinearity. A comprehensive framework that incorporates the above approach is developed in this paper that employs a methodology based on Integral Quadratic Constraints as a means of describing the nonlinearity. It is shown that the developed framework can be used to conclude absolute stability of Lur'e interconnections where all of the existing criteria fail to be satisfied. Indeed, examples are provided where the nonlinearity does not fall into the classes assumed by existing absolute criteria. Another contribution of the article is the extension of IQC theory.

Original languageEnglish (US)
Title of host publication2009 American Control Conference, ACC 2009
Number of pages6
StatePublished - Nov 23 2009
Event2009 American Control Conference, ACC 2009 - St. Louis, MO, United States
Duration: Jun 10 2009Jun 12 2009

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Other2009 American Control Conference, ACC 2009
Country/TerritoryUnited States
CitySt. Louis, MO


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