Abstract. We present an {\it effective method} for the construction of a nonnegative realization of a real coefficient scalar transfer function having a single dominant (positive) pole and complex poles within the spectral disc, {\it all of arbitrary orders}. The nonnegativity of the impulse response is not assumed, but the nonnegativity of the coefficients of the dominant terms in the partial fraction decomposition of the transfer function. If a coefficient in this decomposition is sufficiently large, then a {\it general realization algorithm} is applicable with {\it a priori estimation of the dimension} of the obtained nonnegative realization. {\it An example shows the practical application} of the realization process.

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

Keyword(s): invariant cone, nonnegative realization of a primitive SISO transfer function, a priori estimation of the dimension, multiple complex poles, realization algorithm

Received December 22, 2006, and in revised form December 19, 2007. (Registered under 6003/2009.)