Abstract
Suppose one is given two minimal realizations of the same transfer function matrix. The question is asked: When does there exist a family of coordinate transformations defined by a set of nonsingular matrices <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T(\lambda)</tex> , continuously dependent on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lambda</tex> , with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T(0) = I</tex> and with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(1)</tex> mapping the state vector associated with one minimal realization into the state vector associated with the other? The quesion is answered, and a procedure is given for constructing the family when it exists.
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