Structural invariants of generalized state space systems

In this paper, we present a state space characterization of the transmission zeros of singular linear multivariable systems that is analogous to that of standard systems. We study the structural invariants of a generalized state space model described by the matrix 5-tuple (E, A, B, C, D), where E may be a singular matrix but det(A-λE)≠0. The characterization of these zeros is based on the system matrix of the corresponding 5-tuple and is an extension of equivalent results for state space models described by the 4-tuples (A, B, C, D).