Worst case identification of continuous time systems via interpolation

We consider a worst case robust control oriented identification problem recently studied by several authors. This problem is one of H_∞ identification in the continuous time setting. We give a more general formulation of this problem. The available a priori information in this paper consists of a lower bound on the relative stability of the plant, a frequency dependent upper bound on a certain gain associated with the plant, and an upper bound on the noise level. The available experimental information consists of a finite number of noisy plant point frequency response samples. The objective is to identify, from the given a priori and experimental information, an uncertain model that includes a stable nominal plant model and a bound on the modeling error measured in H_∞ norm. Our main contributions include both a new identification algorithm and several new 'explicit' lower and upper bounds on the identification error. The proposed algorithm belongs to the class of 'interpolatory algorithms' which are known to possess a desirable optimality property under a certain criterion. The error bounds presented improve upon the previously available ones in the aspects of both providing a more accurate estimate of the identification error as well as establishing a faster convergence rate for the proposed algorithm. © 1994.