Input-to-state stability of time-varying nonlinear discrete-time systems via indefinite difference Lyapunov functions

被引：21

作者：

Li, Huijuan ^{[1
]}

Liu, Anping ^{[1
]}

Zhang, Linli ^{[2
]}

机构：

[1] China Univ Geosci Wuhan, Sch Math & Phys, Wuhan 430071, Hubei, Peoples R China

[2] Haikou Coll Econ, Educ Dept Nat Sci, Haikou 571127, Hainan, Peoples R China

来源：

ISA TRANSACTIONS | 2018年 / 77卷

基金：

中国国家自然科学基金;

关键词：

Discrete-time system; Time-varying system; Lyapunov function; Input-to-state stability (ISS); Input-to-state-stable (ISS) Lyapunov function; Indefinite difference Lyapunov function; STABILIZATION;

D O I：

10.1016/j.isatra.2018.03.022

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we propose new sufficient criteria for input-to-state stability (ISS) of time-varying nonlinear discrete-time systems via indefinite difference Lyapunov functions. The proposed sufficient conditions for ISS of system are more relaxed than for ISS with respect to Lyapunov functions with negative definite difference. We prove system is ISS by two methods. The first way is to prove system is ISS by indefinite difference ISS Lyapunov functions. The second method is to prove system is ISS via introducing an auxiliary system and indefinite difference robust Lyapunov functions. The comparison of the sufficient conditions for ISS obtained via the two methods is discussed. The effectiveness of our results is illustrated by three numerical examples. (C) 2018 ISA. Published by Elsevier Ltd. All rights reserved.

引用

页码：71 / 76

页数：6

共 17 条

[1] New asymptotic stability criterion for nonlinear time-variant differential equations [J].

Aeyels, D ;

Peuteman, J .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1998, 43 (07) :968-971

[2] RELAXED ISS SMALL-GAIN THEOREMS FOR DISCRETE-TIME SYSTEMS [J].

Geiselhart, Roman ;

Wirth, Fabian R. .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2016, 54 (02) :423-449

[3]

Jiang Z. P., 2005, IFAC P, V38, P306

[4] Input-to-state stability for discrete-time nonlinear systems [J].

Jiang, ZP ;

Wang, Y .

AUTOMATICA, 2001, 37 (06) :857-869

[5] A converse Lyapunov theorem for discrete-time systems with disturbances [J].

Jiang, ZP ;

Wang, Y .

SYSTEMS & CONTROL LETTERS, 2002, 45 (01) :49-58

[6] A compendium of comparison function results [J].

Kellett, Christopher M. .

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2014, 26 (03) :339-374

[7]

LIN Y., 2005, P 16 IFAC WORLD C PR

[8] Further remarks on strict input-to-state stable Lyapunov functions for time-varying systems [J].

Malisoff, M ;

Mazenc, F .

AUTOMATICA, 2005, 41 (11) :1973-1978

[9]

Malisoff M, 2009, COMMUN CONTROL ENG, P3

[10] Strict Lyapunov functions for time-varying systems [J].

Mazenc, F .

AUTOMATICA, 2003, 39 (02) :349-353

← 1 2 →