Observer-Based Delayed Feedback Control Stabilizing Unstable Periodic Orbits of Continuous-Time Chaotic Systems*

The most important topic in chaos control is the stabilization of unstable periodic orbits (UPOs). The original delayed feedback control (DFC) method has an inherent weak point, called the odd number limitation. In this paper, we introduce a design method involving the use of nonlinear time-delayed observers, which can overcome the odd number limitation, in continuous-time chaotic systems. The proposed method is a natural extension of the discrete-time observer-based DFC method , which is insusceptible to the odd number limitation.