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Kronecker's theory of singular pencils ia applied to multivariable systems in state-space form. The minimal indices and divisors that characterize the theory are related to the system transfer-function matrix through a new canonical form. A new minimal realization procedure based on the infinite divisors of the pencil is given. The concept- of strictly equivalent pencils is used to provide an alternative solution to a model matching problem.

In this paper we present three equivalent characterizations of what can be termed the zeros of a multivariable system. By establishing this equivalence a connection is made between several large bodies of literature on multivariable system problems. In particular, a polynomial which has arisen quite often in recent work on input isolation, decoupling, model matching, etc. is shown to be identical with a numerator polynomial of the Smith McMillan form of a system transfer function matrix. No proofs are presented here but they can be found in a more inclusive paper being submitted for publication [1].