Abstract. Interpretations of most existing controllability and observability notions for linear delay systems are given. Module theoretic characterizations are presented. This setting enables a clear and precise comparison of the various examined notions. A new notion of controllability i s i n troduced, which is called -freeness.
An algebraic framework is proposed for linear systems over Mikusi nski operators. It is illustrated by t h e c o n trol synthesis of an Euler{Bernoulli exible beam. R esum e On propose une th eorie alg ebrique des syst emes lin eaires sur les op erateurs de Mikusi nski, illustr ee par la commande d'une poutre exible d'Euler{Bernoulli.Mots-cl es : syst emes lin eaires, anneaux, modules, commandabilit e, observabilit e, matrices de transfert, op erateurs de Mikusi nski, poutres exibles, equation aux d eriv ees partielles d'Euler{Bernoulli, conjecture de Serre, fonctions de Gevrey-Roumieu.Classi cation math ematique : Primaire 93C20, 73K05, 44A40 Secondaire 13C10, 26E10.
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