On the stability of delayed feedback control of chaos

Author

Nakajima, Hiroyuki ; Ueda, Yoshisuke

Author_Institution

Dept. of Electron. Eng. & Comput. Sci., Kinki Univ., Higashi-Hiroshima, Japan

Volume

3

fYear

1997

fDate

27-29 Aug 1997

Firstpage

411

Abstract

Limitations in controlling chaos in continuous dynamical systems by delayed feedback are proved. The results are as follows: (1) If the linear variational equation about a hyperbolic unstable periodic orbit (UPO) has an odd number of real characteristic multipliers which are greater than unity, the UPO can never be stabilized with any value of feedback gain. (2) If all the characteristic exponents of the variational equation are different from each other and at least one of them is real and positive, then the UPO can never be stabilized with any feedback gain matrix of the form of diag(k, ..., k). These theorems are proved on the basis of Floquet theory. The result of the first theorem is also explained intuitively using bifurcation theory

Keywords

bifurcation; chaos; delays; feedback; hyperbolic equations; matrix algebra; nonlinear dynamical systems; stability; variational techniques; Floquet theory; UPO; bifurcation theory; chaos; continuous dynamical systems; delayed feedback control; feedback gain; feedback gain matrix; hyperbolic unstable periodic orbit; linear variational equation; real characteristic multipliers; stability; variational equation; Bifurcation; Chaos; Computer science; Control systems; Delay effects; Differential equations; Digital-to-frequency converters; Feedback control; Stability; State feedback;

fLanguage

English

Publisher

ieee

Conference_Titel

Control of Oscillations and Chaos, 1997. Proceedings., 1997 1st International Conference

Conference_Location

St. Petersburg

Print_ISBN

0-7803-4247-X

Type

conf

DOI

10.1109/COC.1997.626631

Filename

626631