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.