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Hilbert—Schmidt Systems with Finite-Dimensional State Spaces

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Abstract

The problem of characterizing the input-output behaviour of those linear systems which admit internal representations with finite-dimensional state spaces is studied in this paper. The systems are assumed to be Hilbert-Schmidt systems, and the main result is derived using well-known properties of the kernels of the associated Hankel operators. A necessary and sufficient condition is derived for a system to admit a completely observable and completely accessible internal representation with a finite-dimensional state space.

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