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Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems

journal contribution
posted on 06.03.2013, 16:08 by Alexander N. Gorban, Ivan Tyukin, Erik Steur, Henk Nijmeijer
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.

History

Citation

SIAM Journal on Control and Optimization, forthcoming 2013

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

AM (Accepted Manuscript)

Published in

SIAM Journal on Control and Optimization

Publisher

Society for Industrial and Applied Mathematics (SIAM)

issn

0363-0129

eissn

1095-7138

Copyright date

2013

Publisher version

http://epubs.siam.org/loi/sjcodc

Notes

Embargo length currently unknown. The article is still in press and full text will be made available once it has been published.

Language

en