Vector Spaces of Linearizations for Multivariable State-Space Systems

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