A tight small-gain theorem for not necessarily ISS systems

被引：66

作者：

Angeli, David ^{[1
]}

Astolfi, Alessandro

机构：

[1] Univ Florence, Dept Comp Sci & Syst, Florence, Italy

[2] Univ London Imperial Coll Sci Technol & Med, Dept Elect & Elect Engn, London SW7 2AZ, England

[3] Univ Roma Tor Vergata, Dipartimento Informat Sistemi & Prod, I-00133 Rome, Italy

来源：

SYSTEMS & CONTROL LETTERS | 2007年 / 56卷 / 01期

关键词：

small-gain theorem; input-to-state stability; integral input-to-state stability; global asymptotic stability;

D O I：

10.1016/j.sysconle.2006.08.003

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A new version of the small-gain theorem is presented for nonlinear finite dimensional systems. The result provides conditions for global asymptotic stability under relaxed assumptions, in particular the two interconnected subsystems need not be input-to-state stable in open loop. (c) 2006 Elsevier B.V. All rights reserved.

引用

页码：87 / 91

页数：5

共 13 条

[1]

Clarke F., 1998, NONSMOOTH ANAL CONTR

[2]

Green M., 2012, Linear Robust Control

[3] STABILITY OF NONLINEAR DISSIPATIVE SYSTEMS [J].

HILL, D ;

MOYLAN, P .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1976, 21 (05) :708-711

[4] STABILITY RESULTS FOR NONLINEAR FEEDBACK-SYSTEMS [J].

HILL, DJ ;

MOYLAN, PJ .

AUTOMATICA, 1977, 13 (04) :377-382

[5]

Ito H, 2004, P AMER CONTR CONF, P1055

[6] A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems [J].

Jiang, ZP ;

Mareels, IMY ;

Wang, Y .

AUTOMATICA, 1996, 32 (08) :1211-1215

[7] SMALL-GAIN THEOREM FOR ISS SYSTEMS AND APPLICATIONS [J].

JIANG, ZP ;

TEEL, AR ;

PRALY, L .

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 1994, 7 (02) :95-120

[8] Sufficient conditions for the existence of an unbounded solution [J].

Orsi, R ;

Praly, L ;

Mareels, I .

AUTOMATICA, 2001, 37 (10) :1609-1617

[9] A remark on the stability of interconnected nonlinear systems [J].

Rapaport, A ;

Astolfi, A .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2004, 49 (01) :120-124

[10] SMOOTH STABILIZATION IMPLIES COPRIME FACTORIZATION [J].

SONTAG, ED .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1989, 34 (04) :435-443

← 1 2 →