Robust H2 performance analysis of uncertain lti systems via polynomially parameter-dependent Lyapunov functions

Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Tomomichi Hagiwara

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

8 Citations (Scopus)

Abstract

In this paper, we address the robust H2 performance analysis problems of linear time-invariant polytopic-type uncertain systems. To obtain numerically verifiable and less conservative analysis conditions, we employ polynomially parameter-dependent Lyapunov functions (PPDLFs) to assess the robust H2 performance and give a sufficient condition for the existence of such PPDLFs in terms of finitely many linear matrix inequalities (LMIs). The resulting LMI conditions turn out to be a natural extension of those known as extended or dilated LMIs in the literature, where the PDLFs employed were restricted to those depending affinely on the uncertain parameters. It is shown that, by increasing the degree of PPDLFs, we can obtain more accurate (no more conservative) analysis results at the expense of increased computational burden. Exactness of the proposed analysis conditions as well as their computational complexity will be examined through numerical experiments.

Original languageEnglish
Title of host publicationROCOND'06 - 5th IFAC Symposium on Robust Control Design, Final Program with Abstracts
Pages435-440
Number of pages6
EditionPART 1
Publication statusPublished - Dec 1 2006
Event5th IFAC Symposium on Robust Control Design, ROCOND'06 - Toulouse, France
Duration: Jul 5 2006Jul 7 2006

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
NumberPART 1
Volume5
ISSN (Print)1474-6670

Conference

Conference5th IFAC Symposium on Robust Control Design, ROCOND'06
CountryFrance
CityToulouse
Period7/5/067/7/06

Fingerprint

Uncertain systems
Lyapunov functions
Linear matrix inequalities
Computational complexity
Experiments

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

Cite this

Ebihara, Y., Peaucelle, D., Arzelier, D., & Hagiwara, T. (2006). Robust H2 performance analysis of uncertain lti systems via polynomially parameter-dependent Lyapunov functions. In ROCOND'06 - 5th IFAC Symposium on Robust Control Design, Final Program with Abstracts (PART 1 ed., pp. 435-440). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 5, No. PART 1).

Robust H2 performance analysis of uncertain lti systems via polynomially parameter-dependent Lyapunov functions. / Ebihara, Yoshio; Peaucelle, Dimitri; Arzelier, Denis; Hagiwara, Tomomichi.

ROCOND'06 - 5th IFAC Symposium on Robust Control Design, Final Program with Abstracts. PART 1. ed. 2006. p. 435-440 (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 5, No. PART 1).

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

Ebihara, Y, Peaucelle, D, Arzelier, D & Hagiwara, T 2006, Robust H2 performance analysis of uncertain lti systems via polynomially parameter-dependent Lyapunov functions. in ROCOND'06 - 5th IFAC Symposium on Robust Control Design, Final Program with Abstracts. PART 1 edn, IFAC Proceedings Volumes (IFAC-PapersOnline), no. PART 1, vol. 5, pp. 435-440, 5th IFAC Symposium on Robust Control Design, ROCOND'06, Toulouse, France, 7/5/06.
Ebihara Y, Peaucelle D, Arzelier D, Hagiwara T. Robust H2 performance analysis of uncertain lti systems via polynomially parameter-dependent Lyapunov functions. In ROCOND'06 - 5th IFAC Symposium on Robust Control Design, Final Program with Abstracts. PART 1 ed. 2006. p. 435-440. (IFAC Proceedings Volumes (IFAC-PapersOnline); PART 1).
Ebihara, Yoshio ; Peaucelle, Dimitri ; Arzelier, Denis ; Hagiwara, Tomomichi. / Robust H2 performance analysis of uncertain lti systems via polynomially parameter-dependent Lyapunov functions. ROCOND'06 - 5th IFAC Symposium on Robust Control Design, Final Program with Abstracts. PART 1. ed. 2006. pp. 435-440 (IFAC Proceedings Volumes (IFAC-PapersOnline); PART 1).
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