A direct proof of equivalence of invertibility criteria of multi-variable linear systems†

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Abstract
The purpose of this paper is to give a direct algebraic proof, without invoking the existence of inverse systems, that the two criteria of invertibility of multi-variable linear time-invariant dynamical systems given by Sain and Massey (1969) are equivalent. In a dual manner, the method of this paper can be used to prove directly that the various criteria of functional reproducibility of multi-variable linear systems, which have appeared in the literature, are equivalent.

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