Asymptotic Properties of Input-Output Operators Norm Associated with Singularly Perturbed Systems with Multiplicative White Noise

Abstract

In this paper, we study the problem of the asymptotic property of the norm of input-output operators related to a class of singularly perturbed stochastic linear systems. The system is under perturbation of multiplicative white noise. By using reduction order and boundary layer techniques, it is shown that the norm of the operator of the perturbed system is less than a given number $\gamma$ when the small perturbation $\varepsilon$ tends to zero if both the related norms of the reduced subsystem and the boundary layer subsystem are less than $\gamma$. Furthermore, a stabilizing robust controller is designed, which is independent of perturbation $\varepsilon$.