A Lyapunov Approach to Cascade Interconnection of Integral Input-to-State Stable Systems

被引：81
作者：
Ito, Hiroshi [1 ]
机构：
[1] Kyushu Inst Technol, Dept Syst Design & Informat, Fukuoka 8208502, Japan
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2010年 / 55卷 / 03期
基金：
日本学术振兴会;
关键词：
Cascaded systems; integral input-to-state stability; Lyapunov function; nonlinear systems; SMALL-GAIN THEOREM; UNIFORM ASYMPTOTIC STABILITY; GLOBAL STABILIZATION;
D O I：
10.1109/TAC.2009.2037457
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This technical note deals with the stability of cascade interconnection of integral input-to-state (iISS) time-varying systems. A new technique to construct smooth Lyapunov functions of cascaded systems is proposed. From the construction, sufficient conditions for internal stability and stability with respect to external signals are derived. One of the derived conditions is a trade-off between slower convergence of the driving system and steeper input growth of the driven system. The trade-off is no more necessary if the speed of convergence of the driven system is not radially vanishing. The results are related to trajectory-based approaches and small-gain techniques for feedback interconnection. The difference between the feedback case and the cascade case is viewed from the requirement on convergence speed of autonomous parts.
引用
收藏
页码：702 / 708
页数：7
相关论文
共 25 条
[1]   A characterization of integral input-to-state stability [J].
Angeli, D ;
Sontag, ED ;
Wang, Y .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2000, 45 (06) :1082-1097
[2]   A unifying integral ISS framework for stability of nonlinear cascades [J].
Arcak, M ;
Angeli, D ;
Sontag, E .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2002, 40 (06) :1888-1904
[3]   Integral Input to State Stable Systems in cascade [J].
Chaillet, Antoine ;
Angeli, David .
SYSTEMS & CONTROL LETTERS, 2008, 57 (07) :519-527
[4]  
Dashkovskiy S. N., 2009, SMALL GAIN THEOREMS
[5]   State-dependent scaling problems and stability of interconnected iISS and ISS systems [J].
Ito, Hiroshi .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2006, 51 (10) :1626-1643
[6]   <bold>On Necessary Conditions for Stability of Interconnected iISS Systems</bold> [J].
Ito, Hiroshi ;
Jiang, Zhong-Ping .
2006 AMERICAN CONTROL CONFERENCE, VOLS 1-12, 2006, 1-12 :1499-+
[7]  
Ito H, 2006, IEEE DECIS CONTR P, P357
[8]   Necessary and Sufficient Small Gain Conditions for Integral Input-to-State Stable Systems: A Lyapunov Perspective [J].
Ito, Hiroshi ;
Jiang, Zhong-Ping .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2009, 54 (10) :2389-2404
[9]   Constructive Lyapunov stabilization of nonlinear cascade systems [J].
Jankovic, M ;
Sepulchre, R ;
Kokotovic, PV .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1996, 41 (12) :1723-1735
[10]   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
123