NDLI: A cyclic small-gain condition and an equivalent matrix-like criterion for iISS networks

Content Provider	IEEE Xplore Digital Library
Author	Ito, H. Zhong-Ping Jiang Dashkovskiy, S.N. Ruffer, B.S.
Copyright Year	2012
Description	Author affiliation: Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka 820-8502, Japan (Ito, H.) \|\| Signal and System Theory Group, EIM-E, University of Paderborn, Warburger Str. 100, 33098, Germany (Ruffer, B.S.) \|\| Department of Civil Engineering, University of Applied Sciences Erfurt, Germany (Dashkovskiy, S.N.) \|\| Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Six Metrotech Center, Brooklyn, 11201, USA (Zhong-Ping Jiang)
Abstract	This paper considers nonlinear dynamical networks consisting of individually iISS (integral input-to-state stable) subsystems which are not necessarily ISS (input-to-state stable). Stability criteria for internal and external stability of the networks are developed in view of both necessity and sufficiency. For the sufficiency, we show how we can construct a Lyapunov function of the network explicitly under the assumption that a cyclic small-gain condition is satisfied. The cyclic small-gain condition is shown to be equivalent to a matrix-like condition. The two conditions and their equivalence precisely generalize some central ISS results in the literature. Moreover, the necessity of the matrix-like condition is established. The allowable number of non-ISS subsystems for stability of the network is discussed through several necessity conditions.
Starting Page	4158
Ending Page	4164
File Size	212068
Page Count	7
File Format	PDF
ISBN	9781467320658
ISSN	07431546
e-ISBN	9781467320665
e-ISBN	9781467320641
DOI	10.1109/CDC.2012.6426994
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-12-10
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Lyapunov methods Stability criteria Vectors Educational institutions Nickel USA Councils Indium tin oxide
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Modeling and Simulation

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