H_∞ Identification of Multivariable Systems by Tangential Interpolation Methods

The purpose of this paper is to present an extension to some of the current work on worst-case identification problems to multivariable systems. We consider an H_∞-identification problem for a class of linear shift invariant multi-input/multi-output systems. Our main results are an interpolatory algorithm and a number of bounds on the identification error. This algorithm operates on available input and output data in the time domain and is constructed by solving an extended matrix tangential Carathéodory-Fejér problem. Similar to its counterpart for scalar systems, this interpolatory algorithm possesses certain desirable optimality properties and can be obtained via standard convex programming methods.