An Algebraic Design for the Simultaneous Stabilization of Two Systems
Résumé
In this report we present a unified description for studying the problem of the simultaneous stabilization of two plants. Three approaches for the simultaneous stabilizability are defined. The first one corresponds to the definition commonly used in the literature. For the third one, we show that, like for the first one, the design of a simultaneous compensator leads to a divisibility condition in the ring of $RH_\infty$. A simple formulation of the existence condition for simultaneous stabilization is proposed. Moreover, the equivalence between the existence conditions for the first and third approaches is shown. Finally an explicit method is given to compute simultaneous compensators.