Lyapunov formulation of the ISS cyclic-small-gain theorem for hybrid dynamical networks

被引：22

作者：

Liu, Tengfei ^{[1
]}

Jiang, Zhong-Ping ^{[1
]}

Hill, David J. ^{[2
,3
]}

机构：

[1] NYU, Polytech Inst, Dept Elect & Comp Engn, MetroTech Ctr 6, Brooklyn, NY 11201 USA

[2] Univ Sydney, Sch Elect & Informat Engn, Sydney, NSW 2006, Australia

[3] Natl ICT Australia, Sydney, NSW 2006, Australia

来源：

NONLINEAR ANALYSIS-HYBRID SYSTEMS | 2012年 / 6卷 / 04期

基金：

美国国家科学基金会; 澳大利亚研究理事会;

关键词：

Hybrid nonlinear systems; Dynamical networks; Input-to-state stability; Small-gain; Lyapunov function; TO-STATE STABILITY; LARGE-SCALE; INPUT; SYSTEMS; STABILIZATION;

D O I：

10.1016/j.nahs.2012.07.002

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 paper presents a Lyapunov-based cyclic-small-gain theorem for the hybrid dynamical networks composed of input-to-state stable (ISS) subsystems whose motions may be continuous, impulsive or piecewise constant on the time-line. On the one hand, it is shown that hybrid dynamic networks with interconnection gains less than the identity function are ISS by means of Lyapunov functions. Additionally, an ISS-Lyapunov function for the total network is constructed using the ISS-Lyapunov functions of the subsystems. On the other hand, a novel result of this paper shows that a hybrid dynamic network satisfying the cyclic-small-gain condition can be transformed into one with interconnection gains less than the identity. In sharp contrast with several previously known results, the impulses of the subsystems are time triggered and the impulsive times for different subsystems may be different. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：988 / 1001

页数：14

共 36 条

[1] [Anonymous], 1986, Graph Theory: An Algorithmic Approach
[2] Characterizations of input-to-state stability for hybrid systems
Cai, Chaohong
Teel, Andrew R.
[J]. SYSTEMS & CONTROL LETTERS, 2009, 58 (01) : 47 - 53
[3] An ISS small gain theorem for general networks
Dashkovskiy, Sergey
Rueffer, Bjoern S.
Wirth, Fabian R.
[J]. MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2007, 19 (02) : 93 - 122
[4] Stability of networks of hybrid ISS systems
Dashkovskiy, Sergey
Kosmykov, Michael
[J]. PROCEEDINGS OF THE 48TH IEEE CONFERENCE ON DECISION AND CONTROL, 2009 HELD JOINTLY WITH THE 2009 28TH CHINESE CONTROL CONFERENCE (CDC/CCC 2009), 2009, : 3870 - 3875
[5] SMALL GAIN THEOREMS FOR LARGE SCALE SYSTEMS AND CONSTRUCTION OF ISS LYAPUNOV FUNCTIONS
Dashkovskiy, Sergey N.
Rueffer, Bjoern S.
Wirth, Fabian R.
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2010, 48 (06) : 4089 - 4118
[6] Solutions to hybrid inclusions via set and graphical convergence with stability theory applications
Goebel, R
Teel, AR
[J]. AUTOMATICA, 2006, 42 (04) : 573 - 587
[7] Lyapunov conditions for input-to-state stability of impulsive systems
Hespanha, Joao P.
Liberzon, Daniel
Teel, Andrew R.
[J]. AUTOMATICA, 2008, 44 (11) : 2735 - 2744
[8] A GENERALIZATION OF THE SMALL-GAIN THEOREM FOR NONLINEAR FEEDBACK-SYSTEMS
HILL, DJ
[J]. AUTOMATICA, 1991, 27 (06) : 1043 - 1045
[9] Necessary and Sufficient Small Gain Conditions for Integral Input-to-State Stable Systems: A Lyapunov Perspective
Ito, Hiroshi
Jiang, Zhong-Ping
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2009, 54 (10) : 2389 - 2404
[10] A Generalization of the Nonlinear Small-Gain Theorem for Large-Scale Complex Systems
Jiang, Zhong-Ping
Wang, Yuan
[J]. 2008 7TH WORLD CONGRESS ON INTELLIGENT CONTROL AND AUTOMATION, VOLS 1-23, 2008, : 1188 - +

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