LYAPUNOV DENSITY CRITERIA FOR TIME-VARYING AND PERIODICALLY TIME-VARYING NONLINEAR SYSTEMS WITH CONVERSE RESULTS

被引：3

作者：

Masubuchi, Izumi ^{[1
]}

Kikuchi, Takahiro ^{[2
,3
]}

机构：

[1] Kobe Univ, Grad Sch Syst Informat, Dept Appl Math, Kobe, Hyogo 6578501, Japan

[2] Kobe Univ, Grad Sch Syst Informat, Kobe, Hyogo 6578501, Japan

[3] Shimazu Corp, Kyoto 6048511, Japan

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2021年 / 59卷 / 01期

关键词：

nonlinear time-varying systems; periodically time-varying systems; stability; almost attraction; Lyapunov density; STABILITY; ATTRACTION;

D O I：

10.1137/19M1291479

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper presents criteria for the convergence of trajectories of time-varying nonlinear systems in terms of Lyapunov densities. The results are provided without assuming local stability and forward completeness of trajectories. As well as general time-varying nonlinear systems, periodically time-varying systems are also considered in this paper, where a weaker criterion is proposed for periodically time-varying systems. Also the existence of Lyapunov densities is proved for general and periodic time-varying nonlinear systems under the asymptotic stability of the equilibrium.

引用

页码：223 / 241

页数：19

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