Arbitrary finite spectrum assignment and stabilization of bilinear systems with multiple lumped and distributed delays in state

We consider a bilinear control system defined by a linear time-invariant system of differential equations with multiple lumped and distributed delays in the state variable. A problem of finite spectrum assignment is studied. One needs to construct control vectors such that the characteristic function of the closed-loop system is equal to a polynomial with arbitrary given coefficients. We obtain conditions on coefficients of the system under which the criterion was found for solvability of this finite spectrum assignment problem. This criterion is expressed in terms of rank conditions for matrices of the special form. Corollaries on stabilization of a bilinear system with delays are obtained. An illustrative example is presented.