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A Contraction Theory Approach to Stochastic Incremental Stability

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3 Author(s)
Quang-Cuong Pham ; Lab. de Physiol. de la Perception et de l'' Action, Coll. de France, Paris ; Tabareau, N. ; Slotine, J.-J.

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.

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Automatic Control, IEEE Transactions on  (Volume:54 ,  Issue: 4 )