Analysis of Discrete and Hybrid Stochastic Systems by Nonlinear Contraction Theory

Details Analysis of Discrete and Hybrid Stochastic Systems by Nonlinear Contraction Theory Analysis of Discrete and Hybrid Stochastic Systems by Nonlinear Contraction Theory

2008-04-06

arxiv.org/abs/0804.0934v1

Mathematics

Optimization and Control

6 pages, 1 figure

Scientific paper

We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and hybrid resetting systems. In particular, we show that the mean square distance between any two trajectories of a discrete (or hybrid resetting) contracting stochastic system is upper-bounded by a constant after exponential transients. Using these results, we study the synchronization of noisy nonlinear oscillators coupled by discrete noisy interactions.

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