Pade's Approximation of Sampled Data Controllers

Abstract

In this work we consider a sampled data control system consisting of a continuous time plant and a controller, which is designed as: A uniform sampler plus a discrete time controller plus a zero order hold synchronizer. So, after fixing a sampling period h>0, and in order to take into account the intersampling behaviour of the plant, we apply the lifting technique developed in Bamieh, Dahleh, Pearson: Minimization of the ${\cal L}_\infty$-Induced Norm for Sampled Data Systems. IEEE Transactions on Automatic Control, Vol. 38, No. 5, 1993, pp. 717-732. Next, we consider certain output feedback conditions to construct a biparametric input output operator for the lifted system. Finally, after considering a representation of the family of non-linear and time-varying controllers, we come to our main objective of approaching any infinite-dimensional stabilizing controller by a discrete time but finite dimensional stabilizing one, all that by exhibiting an algorithm based on the theory of Pade's approximating polynomials.