H2-optimal approximation of MIMO linear dynamical systems

Details H2-optimal approximation of MIMO linear dynamical systems H2-optimal approximation of MIMO linear dynamical systems

2008-07-30

arxiv.org/abs/0807.4807v1

Mathematics

Optimization and Control

Paper ID sheet: http://www.inma.ucl.ac.be/~absil/Publi/H2-modred-mimo.htm

Scientific paper

We consider the problem of approximating a multiple-input multiple-output (MIMO) $p\times m$ rational transfer function $H(s)$ of high degree by another $p\times m$ rational transfer function $\hat H(s)$ of much smaller degree, so that the ${\cal H}_2$ norm of the approximation error is minimized. We characterize the stationary points of the ${\cal H}_2$ 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 ${\cal H}_2$ norm of the approximation error for a simple case in order to illustrate the complexity of the minimization problem.

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