Invariant sets of control systems with distributed parameters with time delay

In this paper we consider the problem of finding conditions ensuring that a given set is strong or weak invariant with respect to control system with time delay. System is described by heat conductivity equation in right-hand side of which there is the control in additive form. Necessary and sufficient conditions were obtained for the invariance of a given set under a geometric restriction and sufficient conditions under an integral restriction. The given conditions differ from results for the control with time delay obtained earlier.