多項式型パラメータ体存Lyapunov関数を用いた不確かな線形時不変系のロバスト<i>H</i><sub>∞</sub>性能解析

Translated title of the contribution: Robust <i>H</i><sub>∞</sub> Performance Analysis of Linear Time-Invariant Uncertain Systems via Polynomially Parameter-Dependent Lyapunov Functions

平井 義人, 蛯原 義雄, 萩原 朋道

Research output: Contribution to journalArticle

Abstract

In this paper, we address robust <i>H</i><sub>∞</sub> performance analysis problems of linear time-invariant polytopic-type uncertain systems. We employ polynomially parameter-dependent Lyapunov functions to assess the robust <i>H</i><sub>∞</sub> performance and derive sufficient conditions for the existence of those Lyapunov functions in terms of numerically verifiable finitely many linear matrix inequalities (LMIs). To this end, we first consider to analyze the <i>H</i><sub>∞</sub> performance of uncertainty-free systems by means of Lyapunov functions of a particular form, and explore the existence condition of such Lyapunov functions. We show that, by considering a suitable redundant system description, the existence condition of such Lyapunov functions can be reduced into constrained inequality conditions to which Finsler's Lemma can be applied. It turns that we can readily obtain novel LMI conditions for the <i>H</i><sub>∞</sub> performance analysis of uncertainty-free systems. The LMI-based conditions that enable us to assess the robust <i>H</i><sub>∞</sub> performance of uncertain systems by means of polynomially parameter-dependent Lyapunov functions follow immediately from these newly obtained LMIs. The LMI conditions obtained in this paper can be regarded as a natural extension of those known as extended or dilated LMIs in the literature.
Translated title of the contributionRobust <i>H</i><sub>∞</sub> Performance Analysis of Linear Time-Invariant Uncertain Systems via Polynomially Parameter-Dependent Lyapunov Functions
Original languageUndefined/Unknown
Pages (from-to)618-627
Number of pages10
Journal計測自動制御学会論文集
Volume42
Issue number6
DOIs
Publication statusPublished - 2006

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