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2003 | 13 | 1 | 7-13
Tytuł artykułu

A functorial approach to the behaviour of multidimensional control systems

Treść / Zawartość
Warianty tytułu
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.
Rocznik
Tom
13
Numer
1
Strony
7-13
Opis fizyczny
Daty
wydano
2003
otrzymano
2002-09-01
poprawiono
2003-01-01
Twórcy
  • CERMICS, Ecole Nationale des Ponts et Chaussées, 6 et 8 Avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 02, France
  • 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv13i1p7bwm
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