Spectrum assignment and parametrization of all stabilizing compensators for time-delay systems

The parameterization of the set of all stabilizing compensators for linear systems with commensurate time-delays is discussed. Two definitions of stability are adopted for closed-loop stability: asymptotic stability and finite-spectral stability (which is asymptotic stability with the closed-loop system having only finitely many spectra). Parametrizations of all compensators attaining the closed-loop stability are given. It is noted that, using the parametrizations obtained, one can reduce robust control problems to corresponding interpolation problems