Finite spectrum assignment problem for bilinear systems with several delays

A bilinear control system defined by a linear stationary differential system with several non-commensurate delays in the state variable is considered. A problem of finite spectrum assignment by constant control is studied. One needs to construct constant control vectors such that the characteristic function of the closed-loop system is equal to a polynomial with arbitrary given coefficients. Conditions on coefficients of the system are obtained under which the criterion was found for solvability of the finite spectrum assignment problem. Interconnection of the criterion conditions with the property of consistency for the truncated system without delays is shown. Corollaries on stabilization of bilinear systems with delays are obtained. The similar results are obtained for discrete-time bilinear systems with several delays. An illustrative example is considered.