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-domain techniques: on a derivative feedback approximation idea, and a pole placement idea, respectively. An illustrative example (triple integrator) is presented.