Symmetric formulation of the Kalman-Yakubovich-Popov lemma and exact losslessness condition

Takashi Tanaka, Cedric Langbort

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

Abstract

This paper presents a new algebraic framework for robust stability analysis of linear time invariant systems with an emphasis on symmetry. The main motivation for this work is to provide a unified theory to answer when the the KYP lemma provides an exact LMI test for robust stability. The notions of weak and strong mutual losslessness are introduced to characterize for lossless S-procedures and the KYP lemma. The new framework has sufficient flexibility to unify some recent extensions of the KYP lemma, including the Generalized KYP lemma for finite frequency analysis, the KYP lemma for nD systems, and the diagonal KYP lemma for positive systems. Finally, we show that the new theory also suggests that the structured singular value of internally positive systems with arbitrary number of scalar uncertainties can be exactly computed.

Original languageEnglish (US)
Title of host publication2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Pages5645-5652
Number of pages8
DOIs
StatePublished - Dec 1 2011
Event2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States
Duration: Dec 12 2011Dec 15 2011

Publication series

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

Other

Other2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
CountryUnited States
CityOrlando, FL
Period12/12/1112/15/11

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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