Further Results on Lyapunov Functions for Slowly Time-Varying Systems

Details Further Results on Lyapunov Functions for Slowly Time-Varying Systems Further Results on Lyapunov Functions for Slowly Time-Varying Systems

2006-11-28

arxiv.org/abs/math/0611883v1

Mathematics of Control Signals and Systems, Volume 19, Number 1, pp. 1-21, February 2007

Mathematics

Optimization and Control

Accepted for publication in Mathematics of Control, Signals, and Systems (MCSS) on November 20, 2006

Scientific paper

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.

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