A sufficient condition for the uniform exponential stability of time-varying systems with noise

摘要

The averaging method for nonlinear differential equations with a fast time variable is extended to systems with deterministic bounded noise. The averaged system is used to present a sufficient condition for the uniform exponential stability of the original system. The method of proof is based on a direct computation of the distance of trajectories of the averaged system to trajectories of the original system and manages without smoothness assumptions on the averaged system. (C) 2003 Elsevier Ltd. All rights reserved.