Abstract. The problem of nonnegative realizations of a transfer function (i.e. of a rational matrix function vanishing at infinity) is an important question from the engineering and a highly nontrivial one from the mathematical point of view. We give an upper estimate for the dimension of a nonnegative realization of a primitive scalar transfer function with simple pole at the spectral radius. We show how information on nonnegative realizations of the entries can be used for the upper estimation of the dimension of such realizations of a matrix transfer function.

AMS Subject Classification (1991): 15A48, 15A60, 93B15

Received November 11, 2003, and in revised form June 10, 2004. (Registered under 5829/2009.)