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• W1946294311 abstract "We present a delayed feedback control (DFC) mechanism for stabilizing cycles of one-dimensional discrete time systems. In particular, we consider a DFC for stabilizing -cycles of a differentiable function of the formwhere with . Following an approach of Morgül, we construct a map whose fixed points correspond to -cycles of . We then analyse the local stability of the above DFC mechanism by evaluating the stability of the corresponding equilibrium points of . We associate to each periodic orbit of an explicit polynomial whose Schur stability corresponds to the stability of the DFC on that orbit. This polynomial is the characteristic polynomial of a Jacobian matrix that lies in a large class of matrices that encompasses the usual ‘companion matrices’ found in linear algebra; the primary purpose of this paper is to show that this polynomial may be expressed in a surprisingly simple form. An example indicating the efficacy of this method is provided." @default.
• W1946294311 created "2016-06-24" @default.
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• W1946294311 date "2015-10-29" @default.
• W1946294311 modified "2023-10-16" @default.
• W1946294311 title "On the stability of cycles by delayed feedback control" @default.
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• W1946294311 doi "https://doi.org/10.1080/03081087.2015.1102833" @default.
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