D. Mustafa and T. N. Davidson.
Balanced approximation can be optimal.
Systems & Control Letters,
20(6):397-400, June 1993.
It is shown by example that there exist systems whose balanced approximations are optimal. Specifically, for various norms including the Hankel norm and the ${\cal L}_{2}$ norm, it is shown that the approximation error can achieve the minimum possible.
The paper is available as a pdf file
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