论文信息 - On the equivalence and factorization of multivariate polynomial matrices

On the equivalence and factorization of multivariate polynomial matrices

An important concept in multidimensional (nD) systems and signal processing is that of equivalence of systems, which is closely related to equivalence of multivariate (nD) polynomial matrices. By exploiting recent results on nD polynomial matrix factorizations, this paper presents several new results on the reduction by equivalence of a given nD polynomial matrix to a simpler form. In particular, the new results work for both 2D and nD (n > 2) cases. The paper also discusses equivalence of nD polynomial matrices that are not of normal full-rank, which have received little attention in the past

Zhiping Lin | Li Xu | M. S. Boudellioua

[1] Zhiping Lin,et al. Factorizations fornD polynomial matrices , 2001 .

[2] Zhiping Lin,et al. Notes on n-D Polynomial Matrix Factorizations , 1999, Multidimens. Syst. Signal Process..

[3] D. S. Johnson,et al. A transformation for 2-D linear systems and a generalization of a theorem of Rosenbrock , 1998 .

[4] Dante C. Youla,et al. Notes on n-Dimensional System Theory , 1979 .

[5] Sun-Yuan Kung,et al. New results in 2-D systems theory, part I: 2-D polynomial matrices, factorization, and coprimeness , 1977, Proceedings of the IEEE.

[6] S. Żak,et al. Smith forms over R[z_{1},z_{2}] , 1983 .

[7] M. S. Boudellioua,et al. SOME FURTHER RESULTS CONCERNING MATRICES WITH ELEMENTS IN A POLYNOMIAL RING. , 1986 .

[8] Zhiping Lin. On matrix fraction descriptions of multivariable linear n-D systems , 1988 .

[9] N. Bose,et al. A Generalization of Serre's Conjecture and Some Related Issues , 2001 .

[10] Dengguo Feng,et al. On Lin-Bose problem , 2004 .

[11] M. Morf,et al. New results in 2-D systems theory, part II: 2-D state-space models—Realization and the notions of controllability, observability, and minimality , 1977, Proceedings of the IEEE.