A Contraction Theory Approach to Stochastic Incremental Stability

Author

Pham, Quang-Cuong ; Tabareau, Nicolas ; Slotine, Jean-Jacques

Author_Institution

Lab. de Physiol. de la Perception et de l´´ Action, Coll. de France, Paris

Volume

54

Issue

4

fYear

2009

fDate

4/1/2009 12:00:00 AM

Firstpage

816

Lastpage

820

Abstract

We investigate the incremental stability properties of Ito 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 nonlinear observers design and stochastic synchronization.

Keywords

nonlinear control systems; nonlinear dynamical systems; observers; stability; stochastic systems; synchronisation; mean square distance; noise-free system; nonlinear contraction theory approach; stochastic dynamical system; stochastic incremental stability; Control systems; Convergence; Eigenvalues and eigenfunctions; Nonlinear systems; Stability analysis; Standards development; Stochastic processes; Stochastic resonance; Stochastic systems; Symmetric matrices; Incremental stability; nonlinear contraction theory; stochastic stability;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2008.2009619

Filename

4806161