A fundamental form of equivalence between polynomial matrix descriptions of linear multivariable systems is defined. It is based on the existence of a bijective map between the finite and the infinite solution sets of the differential equations describing the two systems. The connection with the system matrix relationship of full system equivalence is established. It is concluded that the transformation of full system equivalence, with its various characterizations, is the basic transformational tool for the simultaneous study of the finite and infinite frequency behavior of general linear multivariable systems.
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