Robust control and time-domain specifications for systems of delay differential equations via eigenvalue assignment

An approach for eigenvalue assignment for systems of delay differential equations (DDEs), based upon the Lambert W function, is applied to the problem of robust control design for perturbed systems of DDEs, and to the problem of time-domain specifications. The real stability radius, which measures the ability of a system to preserve its stability under a certain class of real perturbations, can be computed from known nominal coefficients of the DDE representing the system. In this paper, considering the stability radius, the real part of the eigenvalues is assigned. Also, time-domain specifications for the transient response of systems of DDEs are improved in a way similar to systems of ordinary differential equations using the eigenvalue assignment approach.