Balanced Realizations in the Wide Sense with a Class of Transfer Functions and Their Low Sensitivity

Abstract

This paper shows that balanced realizations in the wide sense have minimum statistical sensitivity and pole sensitivity, if the transfer functions have interlacing poles and zeros on the real axis of z-plane (i. r. p. z.). If the transfer functions have i. r. p. z., the balanced realizations in the wide sense can be easily obtained by computing the partial fraction expansion of the transfer functions. Since the state transition matrices of the obtained balanced realizations are diagonal, they can be implemented with much fewer parameters than balanced realizations with fully dense coefficient matrices.