Finite spectrum assignment in linear systems with several lumped and distributed delays by means of static output feedback

We consider a control system defined by a linear time-invariant system of differential equations with lumped and distributed delays in the state variable. We construct a controller for the system as linear static output feedback with lumped and distributed delays in the same nodes. We study a finite spectrum assignment problem for the closed-loop system. One needs to construct gain coefficients such that the characteristic function of the closed-loop system becomes a polynomial with arbitrary preassigned coefficients. We obtain conditions on coefficients of the system under which the criterion was found for solvability of the finite spectrum assignment problem. Corollaries on stabilization by linear static output feedback with several delays are obtained for the closed-loop system.