RARL2 is a matlab toolbox. Its goal is to provide  a stable rational L² -approximation of prescribed order to a  H² matrix-valued function  given in one of the following forms

• a finite number of Fourier coefficients
• a state-space realization
• sampled values on the unit circle (frequency data).

It can be used for model reduction, identification from frequency data, pole recovery. It works for MIMO systems.
The optimization method is based on the following points

• the optimization range is reduced to a compact set
• a parametrization of stable all-pass systems is used which guarantees:
  • stability of the approximant
  • degree control
  • well-conditionning

Related publications

• M. Olivi, F. Seyfert, J.P. Marmorat, Identication of microwave filters by analytic and rational H²approximation, Automatica, 49(2013) 317-325
• J.P. Marmorat, M. Olivi, Nudelman Interpolation, Parametrization of Lossless Functions and balanced realizations, Automatica, 43 (2007), 1329-1338
• B. Hanzon, M. Olivi, R.L.M. Peeters, Balanced realizations of discrete-time stable all-pass systems and the tangential Schur algorithm, Linear Algebra and its Applications, 418 (2006), 793-820
• J.P. Marmorat, M. Olivi, B. Hanzon, R. Peeters, Matrix rational H2-approximation: a state-space approach using Schur parameters , CDC02 (Las Vegas) Slides of the presentation
• D. Alpay, L. Baratchart, A. Gombani, On the differential structure of matrix-valued rational inner functions, Operator Theory: Advances and Applications, 73 (1994), 30–66
• L. Baratchart, M. Cardelli, M. Olivi, Identification and rational L2 approximation: a gradient algorithm, Automatica 27(2) (1991), 413-418