Linearizations of Polynomial Matrices with Symmetries and Their Applications.

In E.N. Antoniou and S. Vologiannidis ( 2004), a new family of companion forms associated to a regular polynomial matrix has been presented generalizing similar results presented by M. Fiedler in M. Fiedler (2003) where the scalar case was considered. This family of companion forms preserves both the finite and infinite elementary divisors structure of the original polynomial matrix, thus all its members can be seen as linearizations of the corresponding polynomial matrix. In this note we examine its applications on polynomial matrices with symmetries which appear in a number of engineering fields