INPUT-TO-STATE STABILITY WITH RESPECT TO MEASUREMENT DISTURBANCES FOR ONE-DIMENSIONAL SYSTEMS

Abstract. We consider one-dimensional ane control systems. We show that if such a system is stabilizable by means of a continuous, time-invariant feedback, then it can be made input-to-state stable with respect to measurement disturbances, using a continuous, periodic time-varying feedback. We provide counter-examples showing that the result does not generally hold if we want the feedback to be time-invariant or if the control system is not supposed ane. Resume. Nous etudions des systemes de contrôle anes de dimension un. Nous montrons que si un tel systeme est stabilisable a l’aide d’un feedback continu independant du temps, alors il peut aussi être rendu \input-to-state stable " par rapport aux erreurs de mesure a l’aide d’un feedback continu dependant periodiquement du temps. Nous donnons en outre des contre-exemples montrant que ce resultat est en general faux si on ne considere que des feedbacks independants du temps, ou si le systeme etudie n’est pas ane