文章基本信息

标题：An enhanced stability criterion for linear time-delayed systems via new Lyapunov–Krasovskii functionals
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作者：Wenyong Duan ; Yan Li ; Jian Chen 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-13
DOI：10.1186/s13662-019-2439-z
出版社：Hindawi Publishing Corporation
摘要：The stability problem of linear systems with time-varying delays is studied by improving a Lyapunov–Krasovskii functional (LKF). Based on the newly developed LKF, a less conservative stability criterion than some previous ones is derived. Firstly, to avoid introducing the terms with $h^,(t)$, which are not convenient to directly use the convexity of linear matrix inequality (LMI), the type of integral terms $\{\int _{s}^{t}\dot{x}(u)\,du, \int _{t-h}^{s}\dot{x}(u)\,du\}$ is used in the LKF instead of $\{\int _{s}^{t}x(u)\,du, \int _{t-h}^{s}x(u)\,du\}$. Secondly, two couples of integral terms $\{\int _{s}^{t}\dot{x}(u)\,du, \int _{t-h(t)}^{s}\dot{x}(u)\,du\}$, and $\{\int _{s}^{t-h(t)}\dot{x}(u)\,du, \int _{t-h}^{s}\dot{x}(u)\,du\}$ are supplemented in the integral functionals $\int _{t-h(t)}^{t}\dot{x}(u)\,du$ and $\int _{t-h}^{t-h(t)}\dot{x}(u)\,du$, respectively, so that the time delay, its derivative, and information between them can be fully utilized. Thirdly, the LKF is further augmented by two delay-dependent non-integral items. Finally, three numerical examples are presented under two different delay sets, to show the effectiveness of the proposed approach.
关键词：Delay-dependent stability ; Lyapunov–Krasovskii functional ; Linear matrix inequalities ; Time-delayed system ; Time-varying delay ;