A functorial approach to the behaviour of multidimensional control systems

• Autorzy: Jean-François Pommaret , Alban Quadrat
• Języki publikacji: EN

Abstrakty

EN

We show how to use the extension and torsion functors in order to compute the torsion submodule of a differential module associated with a multidimensional control system. In particular, we show that the concept of the weak primeness of matrices corresponds to the torsion-freeness of a certain module.

Słowa kluczowe

EN

weak primeness; algebraic analysis; multidimensional systems; rings of differential operators; torsion and extension functors; controllability

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2003
• Tom: 13
• Numer: 1
• Strony: 7-13

Daty

wydano

2003

otrzymano

2002-09-01

poprawiono

2003-01-01

Twórcy

autor

Jean-François Pommaret

• CERMICS, Ecole Nationale des Ponts et Chaussées, 6 et 8 Avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 02, France

autor

Alban Quadrat

• INRIA, CAFE project, 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis cedex, France

Bibliografia

• Fornasini E. and Valcher M.E. (1997): nD polynomial matrices with applications to multidimensional signal analysis. - Multidim. Syst. Signal Process., Vol. 8, No. 4, pp. 387-408.
• Kashiwara M. (1970): Algebraic Study of Systems of Partial Differential Equations. - Memoires de la Societe Mathematiques de France, No. 63 (1995).
• Malgrange B. (1966): Ideals of Differential Functions. - Oxford: Oxford University Press.
• Oberst U. (1990): Multidimensional constant linear systems. - Acta Appl. Math., Vol. 20, pp. 1-175.
• Pillai H.K. and Shankar S. (1999): A behavioural approach to control of distributed systems. - SIAM J. Contr. Optim., Vol. 37, No. 2, pp. 388-408.
• Pommaret J.F. (2001): Partial Differential Control Theory. -Dordrecht: Kluwer.
• Pommaret J.F. and Quadrat A. (1999a): Localization and parametrization of linear multidimensional control systems. -Syst. Contr. Lett., Vol. 37, pp. 247-260.
• Pommaret J.F. and Quadrat A. (1999b): Algebraic analysis of linear multidimensional control systems. - IMA J. Contr.Optim., Vol. 16, pp. 275-297.
• Pommaret J.F. and Quadrat A. (2000): Equivalences of linear control systems. - Proc. Int. Symp. Mathematical Theory of Networks and Systems, MTNS 2000, Perpignan, France, (on CD-ROM).
• Quadrat A. (1999): Analyse algebrique des systèmes decontrôle lineaires multidimensionnels. - Ph. D. Thesis, Ecole des Ponts et Chaussees, Marne-La-Vallee, France.
• Quadrat A. (2003): The fractional representation approach to synthesis problems: An algebraic analysis viewpoint, I. (weakly) doubly coprime factorizations, II. internal stabilization. - SIAM J. Contr. Optim., (to appear).
• Rotman J.J. (1979). An Introduction to Homological Algebra. - New York: Academic Press.
• Shankar S. (2001): The lattice structure of behaviours. -SIAM J. Contr. Optim., Vol. 39, No. 6, pp. 1817-1832.
• Smith M.C. (1989): On stabilization and the existence of coprime factorizations. - IEEE Trans. Automat. Contr., Vol. 34, No. 9, pp. 1005-1007.
• Willems J.C. (1991): Paradigms and puzzles in the theory of dynamical systems. - IEEE Trans. Automat. Contr., Vol. 36, No. 3, pp. 259-294.
• Wood J., Rogers E. and Owens D.H. (1998): A formal theory of matrix primeness. - Math. Contr. Signals Syst., Vol. 11, No. 1, pp. 40-78.
• Wood J. (2000): Modules and behaviours in nD systems theory. - Multidim. Syst. Signal Process., Vol. 11, pp. 11-48.