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IMA Journal of Mathematical Control and Information 1986 3(2-3):89-101; doi:10.1093/imamci/3.2-3.89
© 1986 by Institute of Mathematics and its Applications
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Existence and Generic Properties of L2 Approximants for Linear Systems

LAURENT BARATCHART

Institut National de Recherche en Informatique et Automatique Route des Lucioles, Sophia-Antipolis, 06560 Valbonne, France

The problem examined in this paper is the best approximation of a (possibly non-rational) given stable discrete system by a finite-dimensional one, where a bound on the dimension of the approximant is imposed. The criterion is the L2 norm of the transfer function. In this paper, we are interested only in generic qualitative properties of the set of approximants. We first show eixstence. We then prove, for instance, that best approximants are almost always cyclic, and finite in number.


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