![]() In our recent papers, , two schemes were developed to suppress chaos for a class of continuous-time chaotic systems based on the state PI regulator and PI observer methods. However, it is also more complicated than the static DFC, although the dynamic DFC is actually simpler than the observer-based controller. Recently, a dynamic DFC was presented by Yamamoto et al. Konish and Kokame developed an observer-based dynamic control method to overcome the odd eigenvalues number limitation, but the resulting controller is complicated since it requires the design of the state observer. For example, in, the periodic feedback was proposed to overcome the odd eigenvalues number limitation for a class of chaotic systems. To overcome the odd eigenvalues number limitation, several methods have been proposed,. It was also shown by Nakajima that the similar limitation also holds for the continuous-time chaotic systems. This weakness is called the “odd eigenvalues number limitation”. That is, DFC cannot stabilize a target unstable equilibrium point of the discrete-time system if the Jacobian matrix of the linearized system about the unstable equilibrium point has an odd number of real eigenvalues greater than one. DFC has an advantage that it does not require the preliminary calculation of the unstable periodic orbit, but it has some inherent weakness. The delay time τ is equal to the period of the unstable period orbit to be stabilized. Pyragas developed a different control method, called delayed feedback control (DFC) method, in which the control variable is constructed by the difference between the current state and τ-time delayed state. The OGY method and its extension require preliminary calculation of the unstable periodic orbit, so it is inconvenient to apply in real engineering applications,. Ott, Grebogi, and Yorke presented a control method, called the OGY method, for stabilizing the unstable periodic orbits embedded in a chaotic attractor via small control input or perturbation, and several extensions and applications of OGY method have been reported. During recent years, the problem of controlling chaos has received considerable attentions, leading to the development of many methods, ,, ,, ,, ,, ,, ,, ,, ,,. ![]()
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