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TITLE: H2-Optimal linear parametric design
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AUTHORS: Ivan Markovsky, Sabine Van Huffel and Bart De Moor
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ABSTRACT: We consider discrete-time linear time-invariant parameter dependent systems $\tilde H(z,p):=\sum_{i=1}^{n_p}p_iH_i(z)$. The parameter $p$ is a design variable. H2-optimal parametric design problem is defined as $\min_p\norm{\tilde H(z,p)}_2^2$. The solution depends critically on the function $\tilde H(z,\cdot)$. Affine function $\tilde H(z,\cdot)$ corresponds to an open-loop design and leads to a convex quadratic optimization problem. An analytic solution is given in this case. Affine-fractional function $\tilde H(z,\cdot)$ corresponds to a closed-loop design and leads to a non-convex optimization problem. This case remains an open problem.
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STATUS: In the proceedings of the Sixteenth International Symposium on Mathematical Theory of Networks and Systems (MTNS 2004)
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DATE OF ENTRY: April 27, 2001
@InProceedings{MVDM04,
author = {I. Markovsky and S. {Van Huffel} and B. {De Moor}},
title = {{${\cal H}_2$}-optimal linear parametric design},
year = {2004},
booktitle = {CD-ROM proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2004)}
}