Absolute stability for neutral differential systems

This paper is aimed to show that Popov's method for absolute stability, based on the frequency domain approach and the use of Volterra integral equations, can be applied to the case of neutral differential systems of the form (1). The operator A appearing in (1) is formally given by, (2), and it is acting on various function spaces under hypothesis H-1 and H-2 below. The absolute stability for the system (1), (8) is obtained from the corresponding integral equation (15).