Further Results on Lyapunov Functions for Slowly Time-Varying Systems
Optimization and Control
2007-05-23 v1
Abstract
We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily exponentially stable. This complements our previous Lyapunov function constructions for rapidly time-varying dynamics. We also explicitly construct input-to-state stable Lyapunov functions for slowly time-varying control systems. We illustrate our findings by constructing explicit Lyapunov functions for a pendulum model, an example from identification theory, and a perturbed friction model.
Keywords
Cite
@article{arxiv.math/0611883,
title = {Further Results on Lyapunov Functions for Slowly Time-Varying Systems},
author = {Frederic Mazenc and Michael Malisoff},
journal= {arXiv preprint arXiv:math/0611883},
year = {2007}
}
Comments
Accepted for publication in Mathematics of Control, Signals, and Systems (MCSS) on November 20, 2006