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Matrix pencil equivalents of symmetric polynomial matrices

A new family of companion forms for polynomials and polynomial matrices has recently been developed in (Lin. Algebra Appl. 2003; 372: 325–331; Electron. J. Lin. Algebra 2004; 11:78–87) respectively. The application of these new companion forms to polynomial matrices with symmetries has been examined in (Electron. J. Lin. Algebra 2006; 15:107–114). In this work we extend the results presented in (Electron. J. Lin. Algebra 2006; 15:107–114) to the case of 2‐D polynomial matrices. Thus, we provide a new matrix pencil that preserves both the symmetric structure and the structural invariants, of the original 2‐D polynomial matrix. The results are also extended to the polynomial system matrix case. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society