Approximation of Transfer Functions of Infinite Dimensional Dynamical Systems by Rational Interpolants with Prescribed Poles

Rational interpolants with prescribed poles are used to approximate holomorphic functions on the closure of their region of analyticity under natural assumptions of their properties on the boundary. The transfer functions of some infinite dimensional dynamical systems of interest in applications satisfy the restrictions we impose. This is the case for discrete-time fractional filters, time-delay systems, and heat transfer control systems. We give two general results by which, in particular, the transfer functions that arise in such dynamical systems may be approximated. Estimates for the rate of convergence are given. We also include some numerical examples which compare the performance of the method we propose with others commonly used in systems theory.