A Contraction Theory Approach to Stochastic Incremental Stability

We investigate the incremental stability properties of Itô 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...

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Veröffentlicht in:arXiv.org 2008-01
Hauptverfasser: Q -C Pham, Tabareau, N, J -J Slotine
Format: Artikel
Sprache:eng
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Zusammenfassung:We investigate the incremental stability properties of Itô 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.
ISSN:2331-8422