The problem of suppressing chaos in the time-delayed feedback control (TDFC) system is considered. The validity of Melnikov's technique in the planar Hamiltonian system perturbed by weak periodic terms and time-delay terms is discussed. Melnikov's technique is used to analyze a TDFC chaotic system that is nonautonomous. It is revealed with analytical results that the delayed time can be independent of the period of the inherent unstable orbit in the chaotic attractor. Numerical simulations demonstrate the effectiveness of Melnikov's analysis.
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Cai et al. (2002) studied this question.
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