A converse Lyapunov theorem for almost sure stabilizability
Optimization and Control
2007-05-23 v2 Probability
Abstract
We prove a converse Lyapunov theorem for almost sure stabilizability and almost sure asymptotic stabilizability of controlled diffusions: given a stochastic system a.s. stochastic open loop stabilizable at the origin, we construct a lower semicontinuous positive definite function whose level sets form a local basis of viable neighborhoods of the equilibrium. This result provides, with the direct Lyapunov theorems proved in a companion paper, a complete Lyapunov-like characterization of the a.s. stabilizability.
Cite
@article{arxiv.math/0405166,
title = {A converse Lyapunov theorem for almost sure stabilizability},
author = {Annalisa Cesaroni},
journal= {arXiv preprint arXiv:math/0405166},
year = {2007}
}
Comments
11 pages