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Title: Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems
Authors: Gorban, Alexander N.
Tyukin, Ivan
Steur, Erik
Nijmeijer, Henk
First Published: 2013
Publisher: Society for Industrial and Applied Mathematics (SIAM)
Citation: SIAM Journal on Control and Optimization, forthcoming 2013
Abstract: We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable subsystems with one-dimensional unstable dynamics or critically stable dynamics. Systems of this type arise in problems of nonlinear output regulation, parameter estimation and adaptive control. In addition to providing boundedness and convergence criteria the results allow to derive domains of initial conditions corresponding to solutions leaving a given neighborhood of the origin at least once. In contrast to other works addressing convergence issues in unstable systems, our results require neither input-output characterizations for the stable part nor estimates of convergence rates. The results are illustrated with examples, including the analysis of phase synchronization of neural oscillators with heterogenous coupling.
ISSN: 0363-0129
eISSN: 1095-7138
Embargo on file until: 1-Jan-10000
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2013 Society for Industrial and Applied Mathematics. Deposited with reference to the publisher's archiving policy available on the SHERPA/RoMEO website.
Description: Embargo length currently unknown. The article is still in press and full text will be made available once it has been published.
Appears in Collections:Published Articles, Dept. of Mathematics

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