Transformations of system similarity between state-space system matrices over R [s, z]

Abstract

Matrices over R[s, z] which are extensions of the usual form of state-space system matrices over R[s] are considered, the main object being to investigate under what conditions such matrices are system similar over R[z]. It is found that these conditions involve not only the concept of decoupling factors of a system matrix over R[s, z] but also the new concept of decoupling zeros of such a system matrix. The connection of these decoupling zeros for a given system matrix with the corresponding transfer-function matrix is also examined.