Some remarks on stabilizing a chain of integrators using multiple delays

This paper addresses the output feedback stabilization problem of a chain of integrators using multiple delays. We 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.