A Contraction Theory Approach to Stochastic Incremental Stability
Optimization and Control
2011-11-09 v2
Abstract
We investigate the incremental stability properties of It\^o stochastic dynamical systems. Specifically, we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of a stochastically contracting system. This bound can be expressed as a function of the noise intensity and the contraction rate of the noise-free system. We illustrate these results in the contexts of stochastic nonlinear observers design and stochastic synchronization.
Cite
@article{arxiv.0704.0926,
title = {A Contraction Theory Approach to Stochastic Incremental Stability},
author = {Q. -C. Pham and N. Tabareau and J. -J. Slotine},
journal= {arXiv preprint arXiv:0704.0926},
year = {2011}
}
Comments
23 pages, 2 figures