Further Results on Strict Lyapunov Functions for Rapidly Time-Varying Nonlinear Systems
Abstract
We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting dynamics which we assume are uniformly globally asymptotically stable. This leads to new sufficient conditions for uniform global exponential, uniform global asymptotic, and input-to-state stability of fast time-varying dynamics. We also construct strict Lyapunov functions for our systems using a strictification approach. We illustrate our results using a friction control example.
Keywords
Cite
@article{arxiv.math/0601658,
title = {Further Results on Strict Lyapunov Functions for Rapidly Time-Varying Nonlinear Systems},
author = {Frederic Mazenc and Michael Malisoff and Marcio S. de Queiroz},
journal= {arXiv preprint arXiv:math/0601658},
year = {2007}
}
Comments
10 pages, 0 figues, revised and accepted for publication as a regular paper in Automatica in May 2006. To appear in October 2006 issue