On the controllability of linear evolutionary functional-differential systems

New theorem on the controllability of linear functional-differential system of evolutionary type and algorithm for practical verification of controllability are obtained, which can be applied even in the case when the coefficients of system are not continuously differentiable over the time interval under consideration. Special cases of this system are nonstationary systems with distributed and concentrated delay, integro-differential systems with a Voltaire integral and ordinary differential systems. The main results obtained are formulated in the form of 12 theorems and 3 corollaries. On their basis an algorithm for practical verification of the controllability of the system under consideration using a computer is built. Examples illustrating the operability of the obtained theorems and the algorithm are given. The algorithm is implemented in the Maple 17 package for examples of second-order differential systems with delay.