A generalization of the extended delayed feedback control for chaotic systems

Extended delayed feedback control (EDFC) for discrete-time systems is generalized in the following two steps: First, a scalar parameter of the EDFC is generalized to a matrix form. Next, Re allow the matrix to be unstable. Although the power series appeared in the EDFC does not converge with such an unstable parameter, an alternative form of it without the infinite series included is still valid. We call it "generalized extended delayed feedback control (GEDFC)" . We show that the GEDFC is an example of the dynamic DFC, and on the basis of the theory of the dynamic DFC, we prove that the GEDFC with state feedback can stabilize unstable fixed points having the odd number property.