Paper Info
Title
Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems.
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 us 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 heterogeneous coupling.
Year
DOI
Venue
2013
10.1137/120865173
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Keywords
Field
DocType
convergence,weakly attracting sets,Lyapunov functions,synchronization
Convergence (routing),Lyapunov function,Synchronization,Mathematical optimization,Nonlinear system,Invariant (physics),Phase synchronization,Invariant (mathematics),Adaptive control,Mathematics
Journal
Volume
Issue
ISSN
51
3
0363-0129
Citations 
PageRank 
References 
2
0.40
5
Authors
4
Name
Order
Citations
PageRank
Alexander N Gorban19016.13
Ivan Tyukin2719.53
Erik Steur3395.57
Henk Nijmeijer41191161.43