文章基本信息

标题：Refined exponential stability analysis of a coupled system * * The paper was partially supported by the ANR projects LimICoS and SCIDIS. Corresponding author. Fax +33-561336411.
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作者：Mohammed Safi ; Lucie Baudouin ; Alexandre Seuret 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2017
卷号：50
期号：1
页码：11972-11977
DOI：10.1016/j.ifacol.2017.08.1758
语种：English
出版社：Elsevier
摘要：AbstractThe objective of this contribution is to improve recent stability results for a system coupling ordinary differential equations to a vectorial transport partial differential equation by proposing a new structure of Lyapunov functional. Following the same process of most of the investigations in literature, that are based on an a priori selection of Lyapunov functionals and use the usual integral inequalities (Jensen, Wirtinger, Bessel...), we will present an efficient method to estimate the exponential decay rate of this coupled system leading to a tractable test expressed in terms of linear matrix inequalities. These LMI conditions stem from the new design of a candidate Lyapunov functional, but also the inherent properties of the Legendre polynomials, that are used to build a projection of the infinite dimensional part of the state of the system. Based on these polynomials and using the appropriate Bessel-Legendre inequality, we will prove an exponential stability result and in the end, we will show the efficiency of our approach on academic example.
关键词：KeywordsTransport equationLyapunov stabilityintegral inequalities