Input/output-to-state stability and state-norm estimators for switched nonlinear systems

被引：182

作者：

Mueller, Matthias A. ^{[1
]}

Liberzon, Daniel ^{[2
]}

机构：

[1] Univ Stuttgart, Inst Syst Theory & Automat Control, D-70550 Stuttgart, Germany

[2] Univ Illinois, Coordinated Sci Lab, Urbana, IL 61801 USA

来源：

AUTOMATICA | 2012年 / 48卷 / 09期

基金：

新加坡国家研究基金会; 美国国家科学基金会;

关键词：

Switched systems; Input/output-to-state stability (IOSS); State-norm estimators; OUTPUT; STABILIZATION; DETECTABILITY; OBSERVABILITY;

D O I：

10.1016/j.automatica.2012.06.026

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, the concepts of input/output-to-state stability (IOSS) and state-norm estimators are considered for switched nonlinear systems under average dwell-time switching signals. We show that when the average dwell-time is large enough, a switched system is IOSS if all of its constituent subsystems are IOSS. Moreover, under the same conditions, a non-switched state-norm estimator exists for the switched system. Furthermore, if some of the constituent subsystems are not IOSS, we show that still IOSS can be established for the switched system, if the activation time of the non-IOSS subsystems is not too big. Again, under the same conditions, a state-norm estimator exists for the switched system. However, in this case, the state-norm estimator is a switched system itself, consisting of two subsystems. We show that this state-norm estimator can be constructed such that its switching times are independent of the switching times of the switched system it is designed for. (C) 2012 Elsevier Ltd. All rights reserved,

引用

页码：2029 / 2039

页数：11

共 17 条

[1] Forward completeness, unboundedness observability, and their Lyapunov characterizations [J].

Angeli, D ;

Sontag, ED .

SYSTEMS & CONTROL LETTERS, 1999, 38 (4-5) :209-217

[2] Global complete observability and output-to-state stability imply the existence of a globally convergent observer [J].

Astolfi, A ;

Praly, L .

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2006, 18 (01) :32-65

[3] Stability of nonlinear asynchronous systems [J].

de la Pena, David Munoz ;

Christofides, Panagiotis D. .

SYSTEMS & CONTROL LETTERS, 2008, 57 (06) :465-473

[4]

GARCIA RA, 2002, P AMER CONTR CONF, P1892

[5]

Hespanha J. P., 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), P2655, DOI 10.1109/CDC.1999.831330

[6] Input-output-to-state stability [J].

Krichman, M ;

Sontag, ED ;

Wang, Y .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2001, 39 (06) :1874-1928

[7]

Liberzon D., 2003, SYS CON FDN, P190, DOI 10.1007/978-1-4612-0017-8

[8] On the representation of switched systems with inputs by perturbed control systems [J].

Mancilla-Aguilar, JL ;

García, R ;

Sontag, E ;

Wang, Y .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 60 (06) :1111-1150

[9] Supervisory control of families of linear set-point controllers .1. Exact matching [J].

Morse, AS .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1996, 41 (10) :1413-1431

[10] Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stability [J].

Praly, L ;

Wang, Y .

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 1996, 9 (01) :1-33

← 1 2 →