A Contraction Theory Approach to Stochastic Incremental Stability

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...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2009-04, Vol.54 (4), p.816-820
Main Authors: Quang-Cuong Pham, Tabareau, N., Slotine, J.-J.
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control system analysis
Control systems
Control theory. Systems
Convergence
Design engineering
Dynamical systems
Eigenvalues and eigenfunctions
Exact sciences and technology
Incremental stability
Mean square values
Modelling and identification
nonlinear contraction theory
Nonlinear dynamics
Nonlinear systems
Nonlinearity
Stability
Stability analysis
Standards development
Stochastic processes
Stochastic resonance
stochastic stability
Stochastic systems
Stochasticity
Symmetric matrices
Synchronization
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Summary: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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2008.2009619