Realizations in generalized state-space form for polynomial system matrices and the definitions of poles, zeros and decoupling zeros at infinity†

Abstract

This paper contains three main results. Firstly, a realization procedure is presented that brings a polynomial system matrix of a non-proper multivariable system to generalized state-space form, such that all relevant properties including phenomena of redundancy associated with finite and infinite decoupling zeros are retained. Secondly, new definitions are proposed for poles, zeros and decoupling zeros at infinity of a general polynomial system matrix. As a third result, a theorem of Rosenbrock (1974 e) on the redundancy of LCR multiports is generalized to include the decoupling zeros at infinity.