Stabilizing the unstable periodic orbits via improved delayed feedback control for discrete chaotic systems

Delayed feedback control (DFC) is a powerful method for stabilizing unstable periodic orbits embodied in chaotic attractors, but it has an odd number limitation, that is DFC can never stabilize a target unstable periodic orbit of a chaotic system if the transition matrix of the linearized system around the unstable periodic orbit has an odd number of real eigenvalues greater than unity. In this letter, we proposed periodic delayed feedback control method with nonlinear estimation for stabilizing unstable periodic orbits of chaotic discrete-time systems. This method can overcome the inherent weak point of the DFC, and avoid the difficulty of the stabilizing analysis of controlling high-periodic orbits. Periodic feedback gain is derived easily by applying pole-assignment theory.