SINGULAR PERTURBATIONS AND INPUT-TO-STATE STABILITY

This paper establishes a type of total stability for the input-to-stat e stability properly with respect to singular perturbations. In partic ular, if the boundary layer system is uniformly globally asymptoticall y stable and the reduced system is input-to-state stable with respect to disturbances, then these properties continue to hold, up to an arbi trarily small offset, for initial conditions, disturbances, and their derivatives in an arbitrarily large compact set as long as the singula r perturbation parameter is sufficiently small.