Robust Stabilization for a Class of Nonlinear Singularly Perturbed Systems

Abstract

In this paper, the problem of disturbance attenuation with internal stability for a class of nonlinear singularly perturbed systems via nonlinear H∞ approach is studied. It is shown through a useful theorem that under appropriate assumptions, the problem of disturbance attenuation for the main system may be related to the problem of disturbance attenuation for the reduced-order system. This is carried out by a new approach in which we use the quasi-steady state of fast variables. Therefore, the problem of existence of a positive definite solution for the Hamilton–Jacobi–Isaacs (HJI) inequality related to the main system leads to the problem of existence of a solution of a simpler HJI inequality related to the reduced-order system.