Existence of optimal controls for a class of hereditary systems with lagging control

In this paper the problem of existence of optimal controls for a class of time lag systems is considered. It is schown that Oğuztöreli's results (Oğuztöreli, the 8.1, p. 184, “Time Lag Control Systems,≓ Academic Press, New York, 1966) can be extended to a class of time lag systems whose “phase velocity≓ depends also on the past history of control