Stabilizing a chain of integrators using multiple delays

This note addresses the output feedback stabilization problem of a chain of integrators using multiple delays. We shall prove that either n distinct delays or a proportional+delay compensator with n--1 distinct delays are sufficient to stabilize a chain including n integrators. We present two different approaches. Both are constructive and rely on frequency-do-main techniques: on a derivative feedback approximation idea, and a pole placement idea, respectively. An illustrative example (triple integrator) is presented. Index Terms--Delay, integrator, interpolation, pole placement.