70 research outputs found
Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems
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
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