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A Functorial Approach to the Behaviour of Multidimensional Control Systems

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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.
Twórcy
  • CERMICS, Ecole Nationale des Ponts et Chaussées, 6 et 8 Avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 02, France
autor
  • INRIA, CAFE project, 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis cedex, France
Bibliografia
  • [1] 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.
  • [2] Kashiwara M. (1970): Algebraic Study of Systems of Partial Differential Equations. — Mémoires de la Société Mathématiques de France, No. 63 (1995).
  • [3] Malgrange B. (1966): Ideals of Differential Functions. — Oxford: Oxford University Press.
  • [4] Oberst U. (1990): Multidimensional constant linear systems. — Acta Appl. Math., Vol. 20, pp. 1–175.
  • [5] 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.
  • [6] Pommaret J.F. (2001): Partial Differential Control Theory. — Dordrecht: Kluwer.
  • [7] Pommaret J.F. and Quadrat A. (1999a): Localization and parametrization of linear multidimensional control systems.— Syst. Contr. Lett., Vol. 37, pp. 247–260.
  • [8] Pommaret J.F. and Quadrat A. (1999b): Algebraic analysis of linear multidimensional control systems. — IMA J. Contr. Optim., Vol. 16, pp. 275–297.
  • [9] 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).
  • [10] Quadrat A. (1999): Analyse algébrique des systèmes de contrôle linéaires multidimensionnels. — Ph. D. Thesis, Ecole des Ponts et Chaussées, Marne-La-Vallée, France.
  • [11] 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).
  • [12] Rotman J.J. (1979). An Introduction to Homological Algebra.— New York: Academic Press.
  • [13] Shankar S. (2001): The lattice structure of behaviours.—SIAM J. Contr. Optim., Vol. 39, No. 6, pp. 1817–1832.
  • [14] Smith M.C. (1989): On stabilization and the existence of coprime factorizations. — IEEE Trans. Automat. Contr., Vol. 34, No. 9, pp. 1005–1007.
  • [15] Willems J.C. (1991): Paradigms and puzzles in the theory of dynamical systems.—IEEE Trans. Automat. Contr., Vol. 36, No. 3, pp. 259–294.
  • [16] 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.
  • [17] Wood J. (2000): Modules and behaviours in nD systems theory. —Multidim. Syst. Signal Process., Vol. 11, pp. 11–48.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0002-0001
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