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