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

基金：

日本学术振兴会;

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

共 21 条

[1] An almost global notion of input-to-state stability [J].

Angeli, D .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2004, 49 (06) :866-874

[2]

Castan~ eda A., 2015, Journal of Differential Equations, V259, P4364

[3] Attractors of nonlinear dynamical systems with a weakly monotone measure [J].

Grushkovskaya, V. ;

Zuyev, A. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 422 (01) :559-570

[4]

Hoshino K, 2019, 2019 18TH EUROPEAN CONTROL CONFERENCE (ECC), P2608, DOI [10.23919/ecc.2019.8795954, 10.23919/ECC.2019.8795954]

[5]

Karabacak O, 2018, IEEE DECIS CONTR P, P3098, DOI 10.1109/CDC.2018.8618906

[6]

Khalil H. K., 2000, Nonlinear Systems, V3

[7] Analysis of positive invariance and almost regional attraction via density functions with converse results [J].

Masubuchi, Izumi .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2007, 52 (07) :1329-1333

[8]

Masubuchi I, 2017, MED C CONTR AUTOMAT, P169, DOI 10.1109/MED.2017.7984113

[9] A Lyapunov-density criterion for almost everywhere stability of a class of Lipschitz continuous and almost everywhere C1 nonlinear systems [J].

Masubuchi, Izumi ;

Ohta, Yuzo .

INTERNATIONAL JOURNAL OF CONTROL, 2014, 87 (02) :422-431

[10] Almost global attraction in planar systems [J].

Monzón, P .

SYSTEMS & CONTROL LETTERS, 2005, 54 (08) :753-758

← 1 2 3 →