Worst case identification of continuous time systems via interpolation

We consider a worse case control oriented identification problem recently studied by several authors. This problem is one of the H_∞ identification in the continuous time setting. We give a less conservative formulation of this problem. The available apriori information 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 apriori 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 algorithm proposed 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 both the aspects of providing a more accurate estimate of the identification error as well as establishing a faster convergence rate for the proposed algorithm.