Convexity of a set of solutions of a differential inclusion (Q5938984)

It is well known that a transfer from control systems to differential inclusions permits to obtain the essential progress in investigating the control systems themselves. This approach is used in the article and a differential inclusion with retarded arguments is considered. The conditions for the family of solutions of the differential inclusion to be convex in the space of continuous functions are found. The convexity of the solutions is a base property for a prove of sufficient conditions of optimality in form of Pontryagin's maximum principle.