Arbitrary coefficient assignment to the characteristic function of the scalar type for linear systems with state delays by linear static delayed output feedback

We consider a control system defined by a system of linear differential equations in real or complex space with multiple lumped and distributed delays in the state variable. For this system, we study the problem of arbitrary coefficient assignment for the characteristic function of the scalar type by linear static delayed output feedback with lumped and distributed delays. We obtain necessary and sufficient conditions for solvability of the arbitrary coefficient assignment problem by the static delayed output feedback controller when the system coefficients have a special form. Corollaries on arbitrary finite spectrum assignment and on stabilization of the system are obtained. We prove that the obtained results generalize the corresponding theorem proved earlier for a control system defined by a linear delay-differential equation of nth order. Examples are presented illustrating the results obtained.