An equivalent reduction of a 2-D symmetric polynomial matrix

A new family of companion forms for polynomials and polynomial matrices has recently been developed in [4] and [1] respectively. The application of these new companion forms to polynomial matrices with symmetries has been examined in [2]. In this work we extend the results presented in [2] to the case of 2-D polynomial matrices and thus provide a new linearization of a 2-D polynomial matrix that preserves both the symmetric structure and the structural invariants, of the original 2-D polynomial matrix.