Further results on input-to-state stability for nonlinear systems with delayed feedbacks

被引：136
作者：
Mazenc, Frederic [2 ]
Malisoff, Michael [3 ]
Lin, Zongli [1 ]
机构：
[1] Univ Virginia, Charles L Brown Dept Elect & Comp Engn, Charlottesville, VA 22904 USA
[2] INRA, INRIA, Projet MERE, UMR Anal Syst & Biomet, F-34060 Montpellier, France
[3] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
来源：
AUTOMATICA | 2008年 / 44卷 / 09期
基金：
中国国家自然科学基金;
关键词：
delayed systems; input-to-state stability; Lyapunov function constructions;
D O I：
10.1016/j.automatica.2008.01.024
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We consider a class of nonlinear control systems for which stabilizing feedbacks and corresponding Lyapunov functions for the closed-loop systems are available. In the presence of feedback delays and actuator errors, we explicitly construct input-to-state stability (ISS) Lyapunov-Krasovskii functionals for the resulting feedback delayed dynamics, in terms of the available Lyapunov functions for the original undelayed dynamics, which establishes that the closed-loop systems are input-to-state stable (ISS) with respect to actuator errors. We illustrate our results using a generalized system from identification theory and other examples. (C) 2008 Elsevier Ltd. All rights reserved.
引用
收藏
页码：2415 / 2421
页数：7
相关论文
共 16 条
[1]   Delay robustness of a class of nonlinear systems and applications to communication networks [J].
Fan, XZ ;
Arcak, M .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2006, 51 (01) :139-144
[2]  
Fattouh A, 2000, IEEE DECIS CONTR P, P1495, DOI 10.1109/CDC.2000.912070
[3]   Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems [J].
Jankovic, M .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2001, 46 (07) :1048-1060
[4]   Lyapunov theorems for systems described by retarded functional differential equations [J].
Karafyllis, I .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (03) :590-617
[5]  
Khalil HK., 2002, NONLINEAR SYSTEMS, V3rd edition
[6]   Backstepping design for time-delay nonlinear systems [J].
Mazenc, F ;
Bliman, PA .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2006, 51 (01) :149-154
[7]   Further results on strict Lyapunov functions for rapidly time-varying nonlinear systems [J].
Mazenc, Frederic ;
Malisoff, Michael ;
de Queiroz, Marcio S. .
AUTOMATICA, 2006, 42 (10) :1663-1671
[8]  
MICHIELS W, 2002, P 42 IEEE C DEC CONT, P5782
[9]   Input-to-state stability of networked control systems [J].
Nesic, D ;
Teel, AR .
AUTOMATICA, 2004, 40 (12) :2121-2128
[10]   H∞ memoryless control with an α-stability constraint for time-delay systems:: An LMI approach [J].
Niculescu, SI .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1998, 43 (05) :739-743
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