Connections between Realizations of a Transfer Function

Abstract

It is one of the basic facts of linear time-invariant systems theory that any two minimal (canonical) realizations are connected in the best possible way: by system similarity. We study five different types of possible connections between two arbitrary realizations of a transfer function, and are interested in questions of existence (sufficient and/or necessary conditions), uniqueness, and description of all (or of a possibly large class of) connecting operators or pairs of operators. In the case of the existence of nonnegative realizations we seek nonnegative connecting pairs or operators.