Asymptotic disturbance attenuation problem for sampled-data systems

A class of linear shift-invariant discrete systems with disturbances acting on the state variables is considered. Disturbances are assumed to be energy signals. Using singular perturbation theory, a high-gain feedback controller is designed to limit the energy of the disturbances felt at the output. The high-gain feedback controller is designed in two steps and has the following properties: (1) it stabilizes the overall system, (2) it reduces the energy of the disturbances at the output of the slow subsystems within O(∈²), close to a prespecified level, and (3) it reduces the effect of the remaining fast dynamics at the output to an O(∈) quantity