Further Results on Strict Lyapunov Functions for Rapidly Time-Varying Nonlinear Systems

Details Further Results on Strict Lyapunov Functions for Rapidly Time-Varying Nonlinear Systems Further Results on Strict Lyapunov Functions for Rapidly Time-Varying Nonlinear Systems

2006-01-26

arxiv.org/abs/math/0601658v2

Automatica, Volume 42, Issue 10, pp. 1663-1671, October 2006

Mathematics

Optimization and Control

10 pages, 0 figues, revised and accepted for publication as a regular paper in Automatica in May 2006. To appear in October 20

Scientific paper

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.

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