THE CARATHEODORY-FEJER PROBLEM AND H-INFINITY/L(1) IDENTIFICATION - A TIME-DOMAIN APPROACH

In this paper we study a worse-case, robust control oriented identification problem. This problem is in the framework of H(infinity) identification but the formulation here is more general. The available a priori information in our problem consists of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, and an upper bound on the noise level. The plant to be identified is assumed to lie in a certain subset in the space of H(infinity), characterized by the assumed a priori information. The available experimental information consists of a corrupt finite output time series obtained in response to a known nonzero but otherwise arbitrary input. Our objective is to identify from the given a priori and experimental information an uncertain model which consists of a nominal model in H(infinity) and a bound on the modeling error measured in H(infinity) norm. We present both an identification algorithm and several explicit lower and upper bounds on the identification error. The proposed algorithm is in the class of interpolatory algorithms which are known to possess desirable optimality properties in reducing the identification error. This algorithm is obtained by solving an extended Caratheodory-Fejer problem via standard convex programming methods. Both the algorithm and error bounds can be applied to l1 identification problems as well.