Matrix rational H2 approximation: a state-space approach using Schur parameters

This paper deals with the problem of computing a best stable rational L² approximation of specified order to a given multivariable transfer function. The problem is equivalently formulated as a minimization problem over the manifold of stable all-pass (or lossless) transfer functions of fixed order. Some special Schur parameters are used to describe this manifold. Such a description presents numerous advantages: it takes into account the stability constraint, possesses a good numerical behavior and provides a model in state-space form, which is very useful in practice. A rigorous and convergent algorithm is proposed to compute local minima which has been implemented using standard MATLAB subroutines. The effectiveness of our approach to solve model reduction problems as well as identification problems in frequency domain is demonstrated through several examples, including real-data simulations.