H2-optimal approximation of MIMO linear dynamical systems
Abstract
We consider the problem of approximating a multiple-input multiple-output (MIMO) p× m rational transfer function H(s) of high degree by another p× m rational transfer function H(s) of much smaller degree, so that the H2 norm of the approximation error is minimized. We characterize the stationary points of the H2 norm of the approximation error by tangential interpolation conditions and also extend these results to the discrete-time case. We analyze whether it is reasonable to assume that lower-order models can always be approximated arbitrarily closely by imposing only first-order interpolation conditions. Finally, we analyze the H2 norm of the approximation error for a simple case in order to illustrate the complexity of the minimization problem.