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

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.