Singular perturbations and input-to-state stability

This paper establishes a type of total stability for the input-to-state stability property with respect to singular perturbations. In particular, if the boundary layer system is uniformly globally asymptotically stable and the reduced system is input-to-state stable with respect to disturbances, then these properties continue to hold, up to an arbitrarily small offset, for initial conditions, disturbances, and their derivatives in an arbitrarily large compact set as long as the singular perturbation parameter is sufficiently small.