ON APPROXIMATION OF STABLE LINEAR DYNAMICAL-SYSTEMS USING LAGUERRE AND KAUTZ FUNCTIONS

Approximation of stable linear dynamical systems by means of so-called Laguerre and Kautz Functions, which are the Laplace transforms of a c lass of orthonormal exponentials, is studied. Since the impulse respon se of a stable finite dimensional linear dynamical system can be repre sented by a sum of exponentials (times polynomials), it seems reasonab le to use basis functions of the same type. Assuming that the transfer function of a system is bounded and analytic outside a given disc, it is shown that Laguerre basis functions are optimal in a mini-max sens e. This result is extended to the ''two-parameter'' Kautz functions wh ich can have complex poles, while the poles of Laguerre functions are restricted to the real axis. By conformal mapping techniques the ''two -parameter'' Kautz approximation problem is recast as two Laguerre app roximation problems. Thus, the well-developed theory of Laguerre funct ions can be applied to analyze Kautz approx approximations. Unilateral shifts are used to further develop the connection between Laguerre fu nctions and Kautz functions. Results on H-2 and H-infinity, approximat ion using Kautz models are given. Furthermore, the weighted L(2) Kautz approximation problem is shown to be equivalent to solving a block To eplitz matrix equation. Copyright (C) 1996 Elsevier Science Ltd.