Matrix rational H2 approximation and Schur parameters

This paper deals with the rational approximation of specified order n to transfer functions which are assumed to be matrix valued functions in the Hardy space for the complement of the closed unit disk endowed with the L₂-norm. An approach is developed leading to a new algorithm, the first one to our knowledge which concerns matrix transfer functions in L₂-norm. This algorithm proceeds inductively on the order n of the approximant using a gradient algorithm to find local minima through the manifold of inner functions of McMillan degree n. These functions are represented by means of local coordinate maps that come from a matricial version of the Schur algorithm