Asymptotic stability for a class of delay differential inclusions (Q1369867)

Sufficient conditions are obtained for the asymptotic stability of an equilibrium for a class of finite delay-differential inclusions. This class includes inclusions in which the right-hand side is a closed, convex process. The results obtained are related to linear delay-differential equations. However, the conditions are sufficient but not necessary. The author has conjectured that if a condition in this paper is suitably modified, then the conditions become necessary as well as sufficient. Present results partially generalize earlier results of \textit{A. Leizarowitz} [SIAM J. Control Optimization 23, 514-522 (1985; Zbl 0574.49021)]. The paper ends with many interesting questions.