Analytical Limitation for Time-Delayed Feedback Control in Autonomous Systems
نویسندگان
چکیده
منابع مشابه
time - delayed feedback control in autonomous systems
We propose a necessary condition for the successful stabilization of a periodic orbit, using the extended version of time-delayed feedback control. This condition depends on the number of real Floquetmultipliers larger than unity and is therefore related to the wellknown odd-number limitation in non-autonomous systems. We show that the period of the orbit that is induced by mismatching the dela...
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In this paper, the stabilizability problem for chaotic discrete-time systems under the generalized delayed feedback control (GDFC) is addressed. It is proved that 0 < det(I − A) < 2 is a necessary and sufficient condition of stabilizability via m-step GDFC for an n-order system with Jacobi A. The condition reveals the limitation of GDFC more exactly than the odd number limitation. An analytical...
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This chapter reviews the so-called odd number limitation in delayed feedback control (DFC) for chaotic systems. By the odd number limitation, the original DFC restricts the application to a special class of chaotic systems. So far, various methods have been developed to overcome the limitation. In this chapter, we show their key concepts to solve the problem.
متن کاملRefuting the odd-number limitation of time-delayed feedback control.
We refute an often invoked theorem which claims that a periodic orbit with an odd number of real Floquet multipliers greater than unity can never be stabilized by time-delayed feedback control in the form proposed by Pyragas. Using a generic normal form, we demonstrate that the unstable periodic orbit generated by a subcritical Hopf bifurcation, which has a single real unstable Floquet multipli...
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Time-delayed feedback control is an efficient method for stabilizing unstable periodic orbits of chaotic systems. If the equations governing the system dynamics are known, the success of the method can be predicted by a linear stability analysis of the desired orbit. Unfortunately, the usual procedures for evaluating the Floquet exponents of such systems are rather intricate. We show that the m...
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ژورنال
عنوان ژورنال: Physical Review Letters
سال: 2012
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.109.154101