Asymptotic exactness of dual LMI approach for robust performance analysis of uncertain LTI systems

Yoshio Ebihara, Yusuke Matsuda, Tomomichi Hagiwara

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

1 被引用数 (Scopus)

抄録

In the preceding studies we proposed a dual LMI approach for robust performance analysis problems of LTI systems that are affected by parametric uncertainties. By starting from a dual LMI that characterizes a dissipation performance of uncertainty-free LTI systems, we showed that the robust dissipation performance analysis problem can be reduced into a feasibility problem of a polynomial matrix inequality (PMI). Moreover, by applying a linearization to the PMI, we derived an infinite sequence of LMI relaxation problems that allows us to reduce the relaxation gap gradually. Nevertheless, the asymptotic behaviour of this infinite sequence has been open, and this motivates us to study mutual relationship among the dual LMI approach and existing approaches. As the main result of this paper, we prove that our dual LMI approach corresponds to the dual of the polynomial parameter-dependent Lyapunov function approach with matrix sum-of-squares (SOS) relaxations, which is known to be asymptotically exact. Thus we clarify a close relationship between these two approaches that are seemingly very different. This relationship readily leads us to the desired conclusion that the proposed dual LMI approach is asymptotically exact as well.

本文言語英語
ホスト出版物のタイトル2010 49th IEEE Conference on Decision and Control, CDC 2010
出版社Institute of Electrical and Electronics Engineers Inc.
ページ1472-1477
ページ数6
ISBN(印刷版)9781424477456
DOI
出版ステータス出版済み - 2010
外部発表はい
イベント49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, 米国
継続期間: 12 15 201012 17 2010

出版物シリーズ

名前Proceedings of the IEEE Conference on Decision and Control
ISSN(印刷版)0191-2216

会議

会議49th IEEE Conference on Decision and Control, CDC 2010
国/地域米国
CityAtlanta
Period12/15/1012/17/10

All Science Journal Classification (ASJC) codes

  • 制御およびシステム工学
  • モデリングとシミュレーション
  • 制御と最適化

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