Further Results on Lyapunov Functions and Domains of Attraction for Perturbed Asymptotically Stable Systems

Details Further Results on Lyapunov Functions and Domains of Attraction for Perturbed Asymptotically Stable Systems Further Results on Lyapunov Functions and Domains of Attraction for Perturbed Asymptotically Stable Systems

2003-11-16

arxiv.org/abs/math/0311267v2

Dynamics of Continuous Discrete and Impulsive Systems Series A Mathematical Analysis, Volume 12, Number 2, pp. 193-225, 2005

Mathematics

Optimization and Control

33 pages, 0 figures, accepted for publication in Dynamics of Continuous, Discrete, and Impulsive Systems Series A: Mathematica

Scientific paper

We present new theorems characterizing robust Lyapunov functions and infinite
horizon value functions in optimal control as unique viscosity solutions of
partial differential equations. We use these results to further extend Zubov's
method for representing domains of attraction in terms of partial differential
equation solutions.

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