Nous introduisons pour les systèmes linéaires constants les reconstructeurs intégraux et les correcteurs proportionnels-intégraux généralisés, qui permettent d’éviter le terme dérivé du PID classique et, plus généralement, les observateurs asymptotiques usuels. Notre approche, de nature essentiellement algébrique, fait appel à la théorie des modules et au calcul opérationnel de Mikusiński. Plusieurs exemples sont examinés.

For constant linear systems we are introducing integral reconstructors and generalized proportional-integral controllers, which permit to bypass the derivative term in the classic PID controllers and more generally the usual asymptotic observers. Our approach, which is mainly of algebraic flavour, is based on the module-theoretic framework for linear systems and on operational calculus in Mikusiński's setting. Several examples are discussed.

Rings of formal power series $k\left[\right[C\left]\right]$ with exponents in a cyclically ordered group $C$ were defined in [2]. Now, there exists a “valuation” on $k\left[\right[C\left]\right]$ : for every $\sigma$ in $k\left[\right[C\left]\right]$ and $c$ in $C$, we let $v(c,\sigma )$ be the first element of the support of $\sigma$ which is greater than or equal to $c$. Structures with such a valuation can be called cyclically valued rings. Others examples of cyclically valued rings are obtained by “twisting” the multiplication in $k\left[\right[C\left]\right]$. We prove that a cyclically valued ring is a subring of a power series ring $k\left[\right[C,\theta \left]\right]$ with...