A Contraction Theory Approach to Stochastic Incremental Stability

Details A Contraction Theory Approach to Stochastic Incremental Stability A Contraction Theory Approach to Stochastic Incremental Stability

2007-04-06

arxiv.org/abs/0704.0926v2

Mathematics

Optimization and Control

23 pages, 2 figures

Scientific paper

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.

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