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A contraction theory approach to stochastic incremental stability

Abstract : 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.
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https://hal.inria.fr/inria-00466264
Contributor : Nicolas Tabareau <>
Submitted on : Tuesday, March 23, 2010 - 11:43:20 AM
Last modification on : Wednesday, September 23, 2020 - 4:33:04 AM

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Quang-Cuong Pham, Nicolas Tabareau, Jean-Jacques Slotine. A contraction theory approach to stochastic incremental stability. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2009, 54 (4), pp.816--820. ⟨10.1109/TAC.2008.2009619⟩. ⟨inria-00466264⟩

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