A contraction theory approach to stochastic incremental stability

Author(s)
Slotine, Jean-Jacques E.; Pham, Quang-Cuong; Tabareau, Nicolas
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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.
Date issued
2009-04
URI
http://hdl.handle.net/1721.1/54684
Department
Massachusetts Institute of Technology. Department of Mechanical Engineering; Massachusetts Institute of Technology. Nonlinear Systems Laboratory
Journal
IEEE Transactions on Automatic Control
Publisher
Institute of Electrical and Electronics Engineers
Citation
Quang-Cuong Pham, N. Tabareau, and J.-J. Slotine. “A Contraction Theory Approach to Stochastic Incremental Stability.” Automatic Control, IEEE Transactions on 54.4 (2009): 816-820. © 2009 IEEE
Version: Final published version
ISSN
0018-9286
Keywords
stochastic stability, nonlinear contraction theory, Incremental stability
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