A converse Lyapunov theorem for almost sure stabilizability

Details A converse Lyapunov theorem for almost sure stabilizability A converse Lyapunov theorem for almost sure stabilizability

2004-05-10

arxiv.org/abs/math/0405166v2

Mathematics

Optimization and Control

11 pages

Scientific paper

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.

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