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
收藏
页码：223 / 241
页数：19
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