A dissipation inequality formulation for stability analysis with integral quadratic constraints

Peter J Seiler Jr, Andrew Packard, Gary J. Balas

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

14 Scopus citations

Abstract

Integral quadratic constraints (IQCs) provide a general framework for robustness analysis of feedback interconnections. The main IQC stability theorem by Megretski and Rantzer was formulated with frequency domain conditions that depend on the IQC multiplier. Their proof of this theorem uses a homotopy method and operator theory. An interesting aspect of this theory is that input/output stability (defined as uniformly bounded gain over all finite horizons) is established using integral constraints that only hold, in general, on infinite time horizons. The use of IQCs that only hold over infinite time horizons is related to the use of noncausal multipliers in absolute stability theory. This paper shows that if the conditions of the IQC stability theorem are satisfied by any rational IQC multiplier then a dissipation inequality is satisfied by a quadratic storage function. This provides a new interpretation for IQC analysis in terms of quadratic storage functions and a causal, finite-horizon dissipation inequality.

Original languageEnglish (US)
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages2304-2309
Number of pages6
DOIs
StatePublished - Dec 1 2010
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: Dec 15 2010Dec 17 2010

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other2010 49th IEEE Conference on Decision and Control, CDC 2010
CountryUnited States
CityAtlanta, GA
Period12/15/1012/17/10

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