Document Type

Article

Publication Date

10-29-2015

Publication Title

Linear and Multilinear Algebra

DOI

10.1080/03081087.2015.1102833

ISSN

1563-5139

Abstract

We present a delayed feedback control (DFC) mechanism for stabilizing cycles of one dimensional discrete time systems. In particular, we consider a delayed feedback control for stabilizingT-cycles of a differentiable functionf:R→Rof the form

x(k+1)=f(x(k))+u(k)

where

u(k)=(a1−1)f(x(k))+a2f(x(k−T))+...+aNf(x(k−(N−1)T)),

with a1+...+aN=1. Following an approach of Morgül, we construct a map F:RT+1→RT+1 whose fixed points correspond to T-cycles of f. We then analyze the local stability of the above DFC mechanism by evaluating the stability of the corresponding equilibrum points of F. We associate to each periodic orbit of f an explicit polynomial whose Schur stability corresponds to the stability of the DFC on that orbit. An example indicating the efficacy of this method is provided.

Comments

This version of the paper was obtained from arXIV.org. In order for the work to be deposited in arXIV.org, the authors must hold the rights or the work must be under Creative Commons Attribution license, Creative Commons Attribution-Noncommercial-ShareAlike license, or Create Commons Public Domain Declaration. The publisher's final version is available at Linear and Multilinear Algebra.

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