Feedback stabilization of a class of evolution equations with delay

In this paper, we characterize the stabilization of some delay systems. The proof of the main result uses the method introduced in Ammari and Tucsnak (ESAIM COCV 6:361–386, 2001) where the exponential stability for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system combined with a boundedness property of the transfer function of the associated open loop system. The author would like to thank the Institute of Research for Development of France (IRD) and LMDP, the Laboratory of Mathematics and Dynamic of Populations in Marrakesh, for supporting his visit.