Abstract: In an earlier paper by the present authors, a new family of companion forms associated with a regular polynomial matrix was presented, generalizing similar esults by M. Fiedler who considered the scalar case. This family of companion forms preserves both the finite and infinite elementary divisor structure of the original polynomial matrix, thus all its members can be seen as linearizations of the corresponding polynomial matrix. In this note, its applications on
polynomial matrices with symmetries, which appear in a number of engineering fields, are examined.
Abstract: We propose a new algorithm for the computation of a minimal polynomial basis of the left kernel of a given polynomial matrix F(s). The proposed method exploits the structure of the left null space of generalized Wolovich or Sylvester resultants to compute row polynomial vectors that form a minimal polynomial basis of left kernel of the given polynomial matrix. The entire procedure can be implemented using only orthogonal transformations of constant matrices and results to a minimal basis with orthonormal coefficients.
Abstract: In this paper a new family of companion forms associated to a regular polynomial matrix is presented. Similar results have been presented in a recent paper by M. Fiedler, where the scalar case is considered. It is shown that the new 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. Furthermore, for the special class of self-adjoint polynomial matrices a particular member is shown to be self-adjoint itself.
