文章基本信息

标题：Lyapunov Direct Method for Homogeneous Time Delay Systems
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作者：Alexey P. Zhabko ; Irina V. Alexandrova
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2019
卷号：52
期号：18
页码：79-84
DOI：10.1016/j.ifacol.2019.12.210
语种：English
出版社：Elsevier
摘要：In this note, nonlinear time delay systems with homogeneous right-hand sides of degree greater than one and a constant delay are studied. Under an assumption that the corresponding delay free system is asymptotically stable, two criteria for asymptotic stability of the trivial solution based on the Lyapunov-Krasovskii functionals are presented. The first of them is a converse of the well-known Krasovskii theorem under the mentioned assumption whereas in the second one the functional is required to admit a positive definite lower bound on the set of functions satisfying a special condition of Razumikhin type only. The Lyapunov-Krasovskii functionals, which satisfy the conditions of these criteria and are universal within the class of systems under consideration, are constructed. These functionals are based on the Lyapunov functions suitable for analysis of the corresponding delay free systems. They are applied to estimation of the attraction region of solutions of homogeneous systems.
关键词：KeywordsTime delay systemsasymptotic stabilityLyapunov-Krasovskii functionalshomogeneous systemsattraction region