Spectrum Assignment for a System of Neutral Type

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