Title :
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
fDate :
4/1/2009 12:00:00 AM
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;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2008.2009619
