単一の不確定パラメータを有する線形時不変系のロバストH_∞性能解析: 双対LMIに基づく緩和問題の漸近的に厳密な階層的構成と非漸近的な厳密性検証

松田 雄介, 田原 雅人, 蛯原 義雄, 萩原 朋道

研究成果: Contribution to journalArticle査読

抄録

This paper addresses the robust <i>H</i><sub>∞</sub> performance analysis problem of linear time-invariant (LTI) systems whose state-space coefficient matrices depend polynomially on a single uncertain parameter. By means of a dual LMI that characterizes the <i>H</i><sub>∞</sub> performance of uncertainty-free LTI systems, we firstly formulate this analysis problem as a polynomial matrix inequality (PMI) optimization problem. However, this PMI problem is non-convex and hence intractable in general. Therefore, we apply linearization and construct an infinite sequence of relaxation problems, represented by SDPs, with theoretical guarantee of asymptotic exactness in the limit. In order to detect whether an arbitrary relaxation problem in the sequence is “exact” in the sense that it provides the same optimal value as that of the original problem, we derive a rank condition on the SDP solution under which we can conclude the exactness.<br>
寄稿の翻訳タイトルRobust H_∞ Performance Analysis of LTI Systems with a Single Uncertain Parameter: Asymptotically Exact Construction of a Sequence of Relaxation Problems via Dual LMIs and Non-Asymptotic Exactness Verification
本文言語日本語
ページ(範囲)46-55
ページ数10
ジャーナルシステム制御情報学会論文誌
23
3
DOI
出版ステータス出版済み - 3 15 2010

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「単一の不確定パラメータを有する線形時不変系のロバストH_∞性能解析: 双対LMIに基づく緩和問題の漸近的に厳密な階層的構成と非漸近的な厳密性検証」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

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