Séries formelles
La classification chomskienne des langages formels conduit à l'étude d'objets mathématiques nouveaux: les séries rationnelles et algébriques en variables non commutatives.
Séries formelles rationnelles et reconnaissables
Application des variables non commutatives à divers produits de séries formelles
Transductions algébriques
Réalisation locale des systèmes non linéaires, algèbres de Lie filtrées transitives et séries génératrices non commutatives.
Automatique en temps discret et algèbre aux différences.
Automatique et corps différentiels.
Sur divers produits de séries formelles
Décompositions en cascades des systèmes automatiques et feuilletages invariants
On the structure of linear recurrent error-control codes
We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.
Fonctionnelles causales non linéaires et indéterminées non commutatives
Vers une notion de dérivation fonctionnelle causale
Séries rationnelles positives et processus stochastiques
On the structure of linear recurrent error-control codes
We are extending to linear recurrent codes, , to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.
A simple definition of hidden modes, poles and zeros
Some remarks on the Brunovsky canonical form
On a class of linear delay systems often arising in practice
We study the tracking control of linear delay systems. It is based on an algebraic property named -freeness, which extends Kalman’s finite dimensional linear controllability and bears some similarity with finite dimensional nonlinear flat systems. Several examples illustrate the practical relevance of the notion.
Algèbres de Lie nilpotentes, formule de Baker-Campbell-Hausdorff et intégrales itérées de K.T. Chen
An algebraic framework for linear identification
A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.
An algebraic framework for linear identification
A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.
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