Delayed feedback stabilization of unstable equilibria

Analytical results of stabilizing of unstable equilibria of twoand three-dimensional linear systems are presented. The stabilization method is based on time-delayed feedback. Effective necessary and/or sufficient conditions for stabilizing the considered systems in terms of its parameters are obtained. The potential of delayed state and output feedback controls is shown. The theorems proved show that such a delayed feedback approach allows one to extend the possibilities available with static time-invariant state and output feedbacks for stabilizability of unstable linear time-invariant controllable systems. It is used two types of time-delayed feedback: conventional and by Pyragas’ ones. A comparison of the stabilizability domains via both types of feedback is given.