Stabilization by Piragas of discrete systems with the delayed feedback with pulse periodic gain

Authors

  • Gennadiy A. Leonov St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation;
  • Ksenia A. Zvyagintseva St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation;

Abstract

In this paper a method for stabilization of unstable periodic solutions of dynamic systems is proposed. It is based on the delayed feedback with pulse periodic gain which period is twice the period of an orbit being stabilized. Such approach allows one to overcome the restrictions imposed by stabilization with a constant gain. The obtained algorithm is applicable if the linearized system around the cycle has any number of eigenvalues larger than unity. The method is illustrated with the numerical experiments for various discrete systems. Unstable cycles of Cubic, Lozi, and Ricker maps are stabilized. Refs 40. Figs 16.

Keywords:

discrete system, periodic orbit, stabilization, delayed feedback control, asymptotic stability

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Published

2015-08-01

How to Cite

Leonov, G. A., & Zvyagintseva, K. A. (2015). Stabilization by Piragas of discrete systems with the delayed feedback with pulse periodic gain. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2(3), 342–353. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/11168

Issue

Vol. 2 No. 3 (2015)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.