# Abstract:

This paper focuses on the Popov generalized theory for a class of some linear systems including discrete and distributed delays. Sufficient conditions for stabilizing such systems as well as for coerciveness of an appropriate quadratic cost are developed. The obtained results are applied for the design of a {\sl memoryless\/} state feedback control law which guarantees the (exponential) closed-loop stability with an ${\cal L}_2$ norm bound constraint on disturbance attenuation. Note that the proposed results extend similar ones proposed by some of the authors [V. Ionescu, S.I. Niculescu, J.M. Dion, L. Dugard and H. Li: Generalized Popov theory applied to state-delayed systems. In: Proc. 4th IFAC Conf. System Structure Control, Nantes 1998].