Realizability of multilinear input/output maps

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Abstract
This paper examines the realization theory of multilinear input/output maps. It is shown that the existence of a transfer function representation with separable denominator does not guarantee finite state realizability as in the linear and bilinear cases. Conditions for quasi-reachability of a class of multilinear realizations are demonstrated using linear methods, and a form of stability condition obtained for an associated class of multilinear transfer functions. Conditions for observability, which may also be derived from the theory of polynomial response maps, are outlined.

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