Paper ID sheet UCL-INMA-2008.126


H2-Optimal model reduction with higher-order poles

Paul Van Dooren, Kyle A. Gallivan, P.-A. Absil
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 $\mathcal{H}_2$ norm of the approximation error is minimized. We characterize the stationary points of the $\mathcal{H}_2$ 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 $\mathcal{H}_2$ norm of the approximation error for a simple case in order to illustrate the complexity of the minimization problem.
Key words
Multivariable systems; model reduction; optimal $\mathcal{H}_2$ approximation; tangential interpolation
BibTeX entry

  author = "Paul Van Dooren and Kyle A. Gallivan and P.-A. Absil",
  title = "H2-Optimal model reduction with higher-order poles",
  journal = "SIAM J. Matrix Anal. Appl.",
  fjournal = "SIAM Journal on Matrix Analysis and Applications",
  year = 2010,
  volume = 31,
  number = 5,
  pages = "2738-2753",
  doi = "10.1137/080731591",