Some questions of the control theory for functional differential systems

In this paper, some control problems for linear functional differential systems are considered. We are concerned with the problems that arise in various applications including applied problems of mathematical economics and economic dynamics. We pay attention mainly to generalizations of the classic control problem about the transfer of the system from a given initial state to a prescribed terminal state. One of those is the problem of control with respect to a given family of linear functionals. There are proposed conditions of the solvability to the control problem in certain classes of controls including impulse and mixed controls. The problem of impulse correction of classic control is motivated and considered. The key idea of all proposed results is to underline an exclusive role which is played in the discussed questions by the Cauchy matrix of the system under control.