Continuous-time delayed feedback control for chaotic systems using complex number observer

This paper propose a new delayed feedback control (DFC) method which is an extension of the observer-based DFC method to continuous-time cases for the stabilization problem of an unstable periodic orbit (UPO). The proposed method construct a complex-number observer which estimates the tracking error against the UPO. This paper proposes the extension of the author's previous research, and can be used for the time-invariant chaotic systems. The controller tunes the time-shift value of the desired UPO, and overcomes the problem of pole-zero canceling at the origin in the complex plane. The proposed method is applied to the stabilization problem of a UPO in the trajectories of Lorenz model.