A formal theory of matrix primeness

Mathematics of Control, Signals, and Systems

Volumn 11, Issue 1, 1997, Pages 40-78

  Wood, Jeffrey ^a   Rogers, Eric ^a   Owens, David H ^b  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^b UNIVERSITY OF EXETER   (United Kingdom)

Author keywords

Autonomous systems; Behavioural approach; B zout identities; Commutative algebra; Fitting invariants; Gr bner bases; MFDs; Module theory; Multidimensional systems; Primeness

Indexed keywords

IDENTIFICATION (CONTROL SYSTEMS); MATRIX ALGEBRA; POLYNOMIALS;

BEZOUT IDENTITIES; MATRIX PRIMENESS; MODULE THEORY; MULTIDIMENSIONAL SYSTEMS;

CONTROL SYSTEM ANALYSIS;

EID: 0031654883     PISSN: 09324194     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02741885     Document Type: Article

References (36)

1. D. Bayer and M. Stillman. Computation of Hubert functions. Journal of Symbolic Computation, 14 (1992), 31-50.
2. T. Becker and V. Weispfenning. Gröbner Bases: A Computational Approach to Commutative Algebra. Volume 141 of Graduate Texts in Mathematics. Springer-Verlag, Berlin, 1993.
3. B. Buchberger. Gröbner bases: an algorithmic method in polynomial ideal theory. In N. K. Bose, editor, Multidimensional Systems Theory. Reidel, Dordrecht, 1985, pp. 184-232.
4. D. A. Buchsbaum and D. Eisenbud. Some structure theorems for finite free resolutions. Advances in Mathematics, 12 (1974), 84-139.
5. D. Cox, J. Little, and D. O'Shea. Ideals, Varieties and Algorithms, 2nd edition. Springer-Verlag, New York, 1996.
6. D. E. Dudgeon and R. M. Mersereau. Multidimensional Digital Signal Processing. Prentice-Hall, Englewood Cliffs, NJ, 1984.
7. J. Eagon and D. G. Northcott. Ideals defined by matrices, and a certain complex associated to them. Proceedings of the Royal Society, 269 (1962), 188-204.
8. D. Eisenbud. Commutative Algebra with a View Toward Algebraic Geometry. Volume 150 of Graduate Texts in Mathematics. Springer-Verlag, Berlin, 1995.
9. E. Fornasini. A 2-D systems approach to river pollution modelling. Multidimensional Systems and Signal Processing, 2 (1991), 233-265.
10. E. Fornasini, P. Rocha, and S. Zampieri. State space realization of 2-D finite-dimensional behaviours. SIAM Journal of Control and Optimization, 31 (1993), 1502-1517.
11. E. Fornasini and M. E. Valcher. Observability and extendability of finite support nD behaviours. In Proceedings of the 34th IEEE Conference on Decision and Control, Piscataway, NJ. IEEE, New York, 1995, volume 3, pp. 1757-1762.
12. E. Fornasini and M. E. Valcher. nD polynomial matrices with applications to multidimensional signal analysis. Multidimensional Systems and Signal Processing, 8 (1997), 387-408.
13. W. P. Heath and P. E. Wellstead. Self-tuning prediction and control for two-dimensional processes. Part 1: Fixed parameter algorithms. International Journal of Control, 62 (1995), 65-108.
14. D. S. Johnson. Coprimeness in Multidimensional Systems and Symbolic Computation. Ph.D. thesis, Loughborough University of Technology, March 1993.
15. T. Kailath. Linear Systems. Prentice-Hall, Englewood Cliffs, NJ, 1980.
16. S.-Y. Kung, B. C. Levy, M. Morf, and T. Kailath. New results in 2D systems theory. Part II: 2D state-space models - realizations and the notions of controllability, observability and minimality. Proceedings of the IEEE, 65 (1977), 945-961.
17. Z. P. Lin. On MFDs of multivariate linear nD systems. IEEE Transactions on Circuits and Systems, 35 (1988), 1317-1322.
18. M. Morf, B. C. Levy, and S.-Y. Kung. New results in 2D systems theory. Part I: 2D polynomial matrices, factorization and coprimeness. Proceedings of the IEEE, 65 (1977), 861-872.
19. H. Mounier. Propriétés Structurelles des Systèmes Linéaires a Retards: Aspects Théoriques et Pratiques. Ph.D. thesis, Université Paris-Sud, 1995.
20. G. Naadimuthu, K. W. Wang, and E. S. Lee. Air pollution modelling by quasilinearization. Computers & Mathematics with Applications, 21 (1991), 153-164.
21. D. G. Northcott. Finite Free Resolutions. Volume 71 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 1976.
22. U. Oberst. Multidimensional constant linear systems. Acta Applicandae Mathematicae, 20 (1990), 1-175.
23. C. Peskine. An Algebraic Introduction to Complex Projective Geometry. Cambridge University Press, Cambridge, 1996.
24. D. Rees. The grade of an ideal or module. Proceedings of the Cambridge Philosophical Society, 53 (1957), 28-42.
25. P. Rocha. Structure and Representation of 2-D Systems. Ph.D. thesis, University of Groningen, 1990.
26. P. Rocha and J. C. Willems. Controllability of 2-D systems. IEEE Transactions on Automatic Control, 36 (1991), 413-423.
27. E. Rogers and D. H. Owens. Stability Analysis for Linear Repetitive Processes. Volume 175 of Lecture Notes in Control and Information Sciences. Springer-Verlag, Berlin, 1992.
28. H. H. Rosenbrock. State-Space and Multivariable Theory. Nelson, London, 1970.
29. M. Vidyasagar. Control System Synthesis: A Factorization Approach. MIT Press, Cambridge, MA, 1985.
30. J. C. Willems. Paradigms and puzzles in the theory of dynamical systems. IEEE Transactions on Automatic Control, 36 (1991), 259-294.
31. J. Wood, E. Rogers, and D. H. Owens. Controllable and autonomous nD systems. To appear in Multidimensional Systems and Signal Processing, 1998.
32. D. C. Youla and G. Gnavi. Notes on n-dimensional system theory. IEEE Transactions on Circuits and Systems, 26 (1979), 105-111.
33. D. C. Youla and P. F. Pickel. The Quillen-Suslin theorem and the structure of n-dimensional elementary polynomial matrices. IEEE Transactions on Circuits and Systems, 31 (1984), 513-518.
34. S. Zampieri. A solution of the Cauchy problem for multidimensional discrete linear shiftinvariant systems. Linear Algebra and Its Applications, 202 (1994), 143-162.
35. E. Zerz. Primeness of multivariate polynomial matrices. Systems and Control Letters, 29 (1996), 139-146.
36. r. Acta Applicandae Mathematicae, 31 (1993), 249-273.