1 H2 approximation of linear dynamical systems

By P. Van Dooren, K. Gallivan and P.A. Absil.

We consider the problem of approximating an m×p rational transfer function H(s) of high degree by another m×p rational transfer function Ĥ(s) of much smaller degree. We derive the gradients of the H_{2}-norm of the approximation error and show how this can be solved via tangential interpolation. We then extend these results to the discrete-time case, for both time-invariant and time-varying systems.