Observer-predictor based on a PD controller for high-order delayed systems with one unstable pole and n pairs of complex conjugate poles

Abstract

This paper considers the stability of continuous linear systems with time delay. In particular, systems with one unstable pole and n pairs of complex conjugate and/or real poles are analyzed. The proposed solution consists of using an estimated state observer with a closed-loop PD type controller to access to the internal variables of the system. A partition of the time delay is proposed in the observer to addmit the double of the maximum size that when a simple PD controller is considered. The necessary and sufficient conditions for the stability of the proposed control scheme are presented and an example is presented with simulations to demostrate the usefulness of the proposed control strategy.