Vector Spaces of Linearizations for Multivariable State-Space Systems

Abstract

Consider a multivariable state space system and associated transfer function G({\lambda}). The aim of this paper is to define and analyze two vector spaces of matrix pencils associated with the matrix G({\lambda}) and show that almost all of these pencils are linearizations of G({\lambda}). We also construct symmetric/Hermitian linearizations of G({\lambda}) when G({\lambda}) is regular and symmetric/Hermitian.