LMI relaxations for non-quadratic discrete stabilization via pólya theorem

Ji Chang Lo, Chin Fu Tsai

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

In this paper, a relaxation technique based on homogeneous polynomially parameter-dependent (HPPD) solutions to parameter-dependent LMIs (PD-LMIs) is proposed. We investigate non-quadratic relaxed conditions characterized by parameter-dependent LMIs (PD-LMIs) in terms of parameter uncertainty belonging to the unit simplex, exploiting the algebraic property of Pólya's Theorem to construct a family of finite-dimensional LMI relaxations that releases conservatism. Lastly, a numerical experiment to illustrate the advantage of relaxation, being less conservative and reaching exactness, are provided.

Original languageEnglish
Title of host publicationProceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages7430-7435
Number of pages6
ISBN (Print)9781424438716
DOIs
StatePublished - 2009
Event48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China
Duration: 15 Dec 200918 Dec 2009

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Country/TerritoryChina
CityShanghai
Period15/12/0918/12/09

Keywords

  • Homogeneous polynomials
  • Linear matrix inequality (LMI)
  • Parameter-dependent LMIs (PD-LMIs)
  • Relaxation

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