Stability of piecewise linear systems revisited

被引：57
作者：
Sun, Zhendong [1 ]
机构：
[1] S China Univ Technol, Ctr Control & Optimizat, Coll Automat Sci & Engn, Guangzhou 510641, Peoples R China
来源：
ANNUAL REVIEWS IN CONTROL | 2010年 / 34卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Piecewise linear systems; Piecewise quadratic Lyapunov functions; Surface Lyapunov functions; Impact maps; State transition graphs; LYAPUNOV FUNCTIONS; WELL-POSEDNESS; CONTROLLABILITY; AFFINE; CONFIDENCE; NETWORKS; DYNAMICS; DESIGN; AGENTS; SUM;
D O I：
10.1016/j.arcontrol.2010.08.003
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Piecewise linear systems are important in representing and approximating many practical systems with complex dynamics. While stability analysis of switched linear systems are notoriously challenging, several powerful tools have been developed to cope with the challenges. This paper provides a brief survey on stability of piecewise linear systems. The approaches introduced here range from the Lyapunov method to switching-transition-based analysis, and the combined. Main features and advantages of each approach are discussed and compared. Numerical examples and a case study are also presented to illustrate the effectiveness of the approaches. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码：221 / 231
页数：11
相关论文
共 53 条
[31]  
Krause U, 2000, COMMUNICATIONS IN DIFFERENCE EQUATIONS, P227
[32]   Basic problems in stability and design of switched systems [J].
Liberzon, D ;
Morse, AS .
IEEE CONTROL SYSTEMS MAGAZINE, 1999, 19 (05) :59-70
[33]   Continuous opinion dynamics under bounded confidence: A survey [J].
Lorenz, Jan .
INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2007, 18 (12) :1819-1838
[34]  
NAKAMURA A, 1990, 1990 IEEE INTERNATIONAL SYMP ON CIRCUITS AND SYSTEMS, VOLS 1-4, P1454, DOI 10.1109/ISCAS.1990.112406
[35]   A COMMON LYAPUNOV FUNCTION FOR STABLE LTI SYSTEMS WITH COMMUTING A-MATRICES [J].
NARENDRA, KS ;
BALAKRISHNAN, J .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1994, 39 (12) :2469-2471
[36]   A survey on piecewise-linear models of regulatory dynamical systems [J].
Öktem, H .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 63 (03) :336-349
[37]   Consensus problems in networks of agents with switching topology and time-delays [J].
Olfati-Saber, R ;
Murray, RM .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2004, 49 (09) :1520-1533
[38]   Tutorial on sum of squares techniques for systems analysis [J].
Papachristodoulou, A ;
Prajna, S .
ACC: PROCEEDINGS OF THE 2005 AMERICAN CONTROL CONFERENCE, VOLS 1-7, 2005, :2686-2700
[39]  
Prajna S, 2003, P AMER CONTR CONF, P2779
[40]   Fuzzy piecewise multilinear and piecewise linear systems as universal approximators in Sobolev norms [J].
Rovatti, R .
IEEE TRANSACTIONS ON FUZZY SYSTEMS, 1998, 6 (02) :235-249
123456