Singular Perturbation for Sampled-Data Systems With Fast Subsystems

Abstract

We present a sampled-data version of the well-known Tikhonov’s theorem on singular perturbation theory. In particular, we claim that the nonlinear sampled-data systems with fast subsystems can be treated as a singularly perturbed system in a discrete-time sense. In this case, we show that the sampling period can be considered as a singular perturbation parameter. Following the nomenclature of the singular perturbation theory, we define the degenerate (DG) system and the boundary-layer (BL) system and obtain the solution of the sampled-data system as an approximation of the solutions of the lower-order subsystems. Finally, a simple example, sampled-data implementation of disturbance observer, is included to validate the theory.