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标题：Insight into stability analysis of time-delay systems using Legendre polynomials
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作者：M. Bajodek ; A. Seuret ; F. Gouaisbaut 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2020
卷号：53
期号：2
页码：4816-4821
DOI：10.1016/j.ifacol.2020.12.1029
语种：English
出版社：Elsevier
摘要：AbstractIn this paper, a numerical analysis to assess stability of time-delay systems is investigated. The proposed approach is based on the design of a finite-dimensional approximation of the infinite-dimensional space of solutions of the system. Indeed, based on the dynamical coefficients on the sequence made of the first Legendre polynomials, the original time-delay system is modelled by a finite-dimensional model interconnected to a modelling error.Putting aside the interconnection, the resulting finite-dimensional system turns out to be a nice approximation of the time-delay system. Using Padé arguments, the eigenvalues of this finite-dimensional system are proven to converge towards a set of characteristic roots of the original time-delay system. Furthermore, considering now the whole interconnected system and having a deeper look at the interconnection, an enriched Lyapunov-Krasovskii functional is proposed to develop a sufficient condition expressed in terms of linear matrix inequalities for the stability of the time-delay system. Both results are illustrated on a toy example.
关键词：KeywordsTime-delayNumerical analysisEigenvaluesLyapunov stabilityLMI