Canonical forms and parametrizations are presented for several sets of minimal systems of given dimension: asymptotically stable systems, allpass systems, bounded real systems, positive real systems, minimum-phase systems, and the class of all minimal systems. The approach is based on balancing techniques for these classes of systems. Applications of these results to Hankel operators and model reduction are discussed.
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Raimund J. Ober (1991) studied this question.
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