Stabilization of n-order Unstable Linear Delayed Systems with Possible Complex Conjugate Poles

This work considers the stabilization problem of n-order unstable linear systems with time-delay, specifically with one unstable pole and the resting n – 1 stables poles, which can be complex conjugate. Necessary and sufficient conditions are stated to guarantee the stability of the closed loop delayed system by means of a static output feedback. Likewise, using the above result, it is proposed a Predictor Scheme, which improves the transient behavior of the system. Finally, the performance of the proposed control strategy is evaluated by numerical simulation in the application to an academic example.