Spectrum Assignment for a System of Neutral Type

For a linear autonomous system of neutral type with commensurable delays, an algorithm is given for solving the modal controllability problem (in particular, the finite spectrum assignment problem), which provides a closed-loop system with a given characteristic quasipolynomial. A procedure for editing the finite part of the spectrum is proposed. A criterion for exponential stabilization of the system under study is constructively justified. When the criterion is met, the closed-loop system can be made exponentially stable according to the proposed spectral reduction algorithm. The obtained statements and spectrum assignment algorithms are illustrated with examples.