Exponential stability of singularly perturbed stochastic systems

The sufficient conditions of exponential stability of singularly perturbed, nonlinear stochastic systems are established. The excitations are assumed to be parametric white noises. In this case, the objective is to analyze the full-order system in their lower order subsystems, i.e., the reduced-order system and the boundary-layer system, and in terms of their interconnecting structure and the perturbation parameter varepsilon. The exponential bounds depend on the moments of norms of trajectories given for the "slow" and "fast" components of the full-order system. The estimation of the rate of convergence of the full-order system is also shown.