Linear systems with commensurate time delays: stability and stabilization independent of delay

Notions of exponential stability independent of delay and stabilizability independent of delay are developed for the class of delay differential systems of the retarded type with commensurate time delays. Various criteria for exponential stability independent of delay with a given order are specified in terms of matrices whose entries are functions of a single real parameter and polynomials in one variable whose coefficients are functions of a single real parameter. Sufficient conditions and a necessary condition based on local stabilizability are given for stabilizability independent of delay using state feedback with commensurate time delays. Constructive methods for determining a stabilizing feedback are also presented. The last part of the paper deals with a standard type of observer and regulator with the requirement that the closed-loop system be stable independent of delay.