Optimal approximation of continuous-time systems

In [1], the problem of optimally approximating a discrete-time system by a lower-order system was solved based on a remarkable theoretical result of Adamjan, Arov and Krein [2]. In this paper, we derive similar reduced models for continuous-time systems using a new approach based on the system structure of the finite dimensional model. Concrete algorithms are developed for finding approximations of any specified order. These approximations are optimal in a well defined sense.