Dynamic delayed feedback controllers for chaotic discrete-time systems

Delayed feedback control (DFC), proposed by Pyragas [1992], is one of the useful control methods for chaotic systems. However, this static DFC has a limitation such that it can not stabilize any systems with an odd number of real eigenvalues greater than unity. In this paper, to overcome the limitation we introduce dynamic delayed feedback, and derive a necessary and sufficient condition for stabilization of such chaotic systems. Moreover, it is shown that the order of the dynamic delayed feedback controller is not necessarily greater than that of the chaotic system. Furthermore, we show a method of designing reduced-order controllers which is based on the linear matrix inequalities.