We describe a new approach of the generalized Bezout identity for linear time-varying ordinary differential control systems. We also explain when and how it can be extended to linear partial… (More)

We show how homological algebra and algebraic analysis allow to give various notions of equivalence for linear control systems which do not depend on their presentations and therefore preserve their… (More)

The present chapter contains the material taught within the module P2 of FAP 2004. The purpose of this intensive course is first to provide an introduction to “algebraic analysis”. This fashionable… (More)

The conjecture proposed by J.P. Serre in 1955 saying that a projective module over a polynomial ring is free has been solved independently in 1976 by D. Quillen and A.A. Suslin. As a generalization… (More)

X= manifold with local coordinates (x), i = 1, ..., n = dim(X) G= Lie group with local coordinates (a ), τ = 1, ..., p = dim(G) Lie group action : X ×G −→ X ×X : (x, a) −→ (x, y = ax = f(x, a))… (More)

We use recent improvements in the parametrizations of controllable linear multidimensional systems to show how to transform the study of a linear quadratic optimal problem into that of a variational… (More)

Observation problems in control systems literature generally refer to problems of estimation of state variables (or identification of model parameters) from two sources of information: dynamic models… (More)

We study the link existing between the parametrization of diierential operators by potential like arbitrary functions and the localization of diierential modules, while applying these results to the… (More)

The first purpose of this paper is to point out a curious result announced by Macaulay on the Hilbert function of a differential module in his famous book The Algebraic Theory of Modular Systems… (More)