Some Results on the Relationship Between Two-Dimensional Behaviors Decompositions and the Factor Skew-Primeness Property

In this paper, the possibility of obtaining certain decompositions with finite-dimensional intersection, for a given complete two-dimensional behavior, is investigated and related to the factor skew-primeness property of certain matrix pairs involved in the behavior description. The analysis carried on here leads to some preliminary results, which extend those about direct sum decompositions presented in [1].

[1]  Li Xu,et al.  Bilateral polynomial matrix equations in two indeterminates , 1990, Multidimens. Syst. Signal Process..

[2]  Michael Sebek,et al.  Two-sided equations and skew primeness for n -D polynomial matrices , 1989 .

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

[4]  William A. Wolovich,et al.  Skew prime polynomial matrices , 1978 .

[5]  U. Oberst.  Multidimensional constant linear systems , 1990, EUROCAST.

[6]  Maria Elena Valcher,et al.  On the Decomposition of Two-Dimensional Behaviors , 2000, Multidimens. Syst. Signal Process..

[7]  Maria Elena Valcher,et al.  Behavior decompositions and two-sided diophantine equations , 2001, Autom..

[8]  Jan C. Willems,et al.  Models for Dynamics , 1989 .

[9]  Eric Rogers,et al.  Controllable and Autonomous nD Linear Systems , 1999, Multidimens. Syst. Signal Process..

[10]  Maria Elena Valcher,et al.  Characteristic cones and stability properties of two-dimensional autonomous behaviors , 2000 .

[11]  J. Willems,et al.  Canonical computational forms for AR 2-D systems , 1990, Multidimensional systems and signal processing.

[12]  S. Zampieri,et al.  State space realization of 2-D finite-dimensional behaviours , 1993 .

[13]  Maria Elena Valcher,et al.  A note on the direct sum decomposition of two-dimensional behaviors , 2001 .

[14]  E. Fornasini,et al.  Multidimensional Systems with Finite Support Behaviors: Signal Structure, Generation, and Detection , 1998 .

[15]  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.

[16]  Jan C. Willems,et al.  Introduction to mathematical systems theory: a behavioral approach, Texts in Applied Mathematics 26 , 1999 .

[17]  Ettore Fornasini,et al.  nD Polynomial Matrices with Applications to Multidimensional Signal Analysis , 1997, Multidimens. Syst. Signal Process..

[18]  Vincent D. Blondel,et al.  Probabilistic solutions to some NP-hard matrix problems , 2001, Autom..

[19]  Maria Paula Macedo Rocha.  Structure and representation of 2-D systems , 1990 .

[20]  W. E. Roth,et al.  The equations $AX-YB=C$ and $AX-XB=C$ in matrices , 1952 .