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  1. Mathematics of Control, Signals, and Systems
  2. Mathematics of Control, Signals, and Systems : Volume 19
  3. Mathematics of Control, Signals, and Systems : Volume 19, Issue 2, May 2007
  4. An ISS small gain theorem for general networks
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Mathematics of Control, Signals, and Systems : Volume 29
Mathematics of Control, Signals, and Systems : Volume 28
Mathematics of Control, Signals, and Systems : Volume 27
Mathematics of Control, Signals, and Systems : Volume 26
Mathematics of Control, Signals, and Systems : Volume 25
Mathematics of Control, Signals, and Systems : Volume 24
Mathematics of Control, Signals, and Systems : Volume 23
Mathematics of Control, Signals, and Systems : Volume 22
Mathematics of Control, Signals, and Systems : Volume 21
Mathematics of Control, Signals, and Systems : Volume 20
Mathematics of Control, Signals, and Systems : Volume 19
Mathematics of Control, Signals, and Systems : Volume 19, Issue 4, November 2007
Mathematics of Control, Signals, and Systems : Volume 19, Issue 3, August 2007
Mathematics of Control, Signals, and Systems : Volume 19, Issue 2, May 2007
An ISS small gain theorem for general networks
On the embedding of state space realizations
Lyapunov functions for time-varying systems satisfying generalized conditions of Matrosov theorem
Mathematics of Control, Signals, and Systems : Volume 19, Issue 1, February 2007
Mathematics of Control, Signals, and Systems : Volume 18
Mathematics of Control, Signals, and Systems : Volume 17
Mathematics of Control, Signals, and Systems : Volume 16
Mathematics of Control, Signals, and Systems : Volume 15
Mathematics of Control, Signals, and Systems : Volume 14
Mathematics of Control, Signals, and Systems : Volume 13
Mathematics of Control, Signals, and Systems : Volume 12
Mathematics of Control, Signals, and Systems : Volume 11
Mathematics of Control, Signals, and Systems : Volume 10

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An ISS small gain theorem for general networks

Content Provider SpringerLink
Author Dashkovskiy, Sergey Rüffer, Björn S. Wirth, Fabian R.
Copyright Year 2007
Abstract We provide a generalized version of the nonlinear small gain theorem for the case of more than two coupled input-to-state stable systems. For this result the interconnection gains are described in a nonlinear gain matrix, and the small gain condition requires bounds on the image of this gain matrix. The condition may be interpreted as a nonlinear generalization of the requirement that the spectral radius of the gain matrix is less than 1. We give some interpretations of the condition in special cases covering two subsystems, linear gains, linear systems and an associated lower-dimensional discrete time dynamical system.
Starting Page 93
Ending Page 122
Page Count 30
File Format PDF
ISSN 09324194
Journal Mathematics of Control, Signals, and Systems
Volume Number 19
Issue Number 2
e-ISSN 1435568X
Language English
Publisher Springer-Verlag
Publisher Date 2007-05-08
Publisher Place London
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Interconnected systems Input-to-state stability Small gain theorem Large-scale systems Monotone maps Control Engineering Communications Engineering, Networks Mathematics
Content Type Text
Resource Type Article
Subject Control and Optimization Applied Mathematics Signal Processing Control and Systems Engineering
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