Asymptotic Stability for a Class of Delay Differential Inclusions

In this work we provide sufficient conditions for the asymptotic stability of an equilibrium for a class of differential inclusions of finite retarded type where the right-hand side is a set-valued mapping having a bounded, closed, convex graph. In particular our result includes “linear differential inclusions” in which the right-hand side is a closed, convex process. This result partially generalizes an earlier result of Leizarowitz (1985,SIAM J. Control Optim.23, 514–522) in the non-delay case.