Construction of Lyapunov functions for piecewise-deterministic Markov processes

The purpose of this contribution is twofold: 1) to present for the first time a Lyapunov function that proves exponential ergodicity of a process studied by the authors in, where the problem of controlling the probability density of a swarm of robotic agents was solved; 2) to introduce alongside the method used to construct this Lyapunov function, which is of interest in its own since it may be applicable to a wide class of piecewise-deterministc Markov processes. Our method searches for the Lyapunovfunction that maximizes a measure of the rate of convergence that appears in the theory of large deviations. Analytical solutions are often possible as shown by examples.

Mesquita, A., Hespanha, J.
Proceedings of the 49th IEEE Conference on Decision and Control
Pages: 2408 - 2413
City: Atlanta
State: GA
Date: December, 2010
ICB Affiliated Authors: João P Hespanha