Stochastic Stability of Singularly Perturbed Nonlinear Systems
نویسنده
چکیده
The stability of a nonlinear stochastic dynamic system with singular perturbations is considered. Based on the notion of stochastic input-to-state stability and using time scale decomposition, a result of the total stability type is obtained, i.e. if the fast subsystem and the slow subsystem are both input-to-state stable with respect to disturbances, then this property continues to hold for the full-order system as long as the singular perturbation parameter is su ciently small and a stochastic small gain condition is satis ed. The result is general in that it holds for a broad class of disturbances, and resembles similar results for deterministic systems.
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