On controllability of algebraic integral systems with a kernel of the convolution type

Controlled systems of integral equations of the from Ax+Vx=Bu, where V is the Volterra operator with a kernel of the convolution type, are considered. Here A,B are constant matrices and detA=0. The existence theorem has been proved and necessary and sufficient conditions, under which the kernel of the system is trivial, have been established. It has been investigated as to under what conditions linear combinations of x take on given values.