Mathematics of Control, Signals and Systems

, Volume 13, Issue 3, pp 193–215

Formal Elimination for Multidimensional Systems and Applications to Control Theory

  • J. F. Pommaret
  • A. Quadrat

DOI: 10.1007/PL00009867

Cite this article as:
Pommaret, J. & Quadrat, A. Math. Control Signals Systems (2000) 13: 193. doi:10.1007/PL00009867

Abstract.

Following Douglas's ideas on the inverse problem of the calculus of variations, the purpose of this article is to show that one can use formal integrability theory to develop a theory of elimination for systems of partial differential equations and apply it to control theory. In particular, we consider linear systems of partial differential equations with variable coefficients and we show that we can organize the integrability conditions on the coefficients to build an “intrinsic tree”. Trees of integrability conditions naturally appear when we test the structural properties of linear multidimensional control systems with some variable or unknown coefficients (controllability, observability, invertibility, …) or for generic linearization of nonlinear systems.

Key words. Elimination theory, Multidimensional linear control systems with variable or unknown coefficients, Generic linearization of nonlinear control systems, Structural properties of control systems, Controllability, Trees of integrability conditions, Formal integrability, Differential modules.

Copyright information

© Springer-Verlag London Limited 2000

Authors and Affiliations

  • J. F. Pommaret
    • 1
  • A. Quadrat
    • 1
  1. 1.CERMICS, Ecole Nationale des Ponts et Chaussées, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 02, France. {pommaret, quadrat}@cermics.enpc.fr.FR