Limitation of delayed feedback control in nonlinear discrete-time systems

Author

Ushio, Toshimitsu

Author_Institution

Dept. of Electron. Eng., Osaka Univ., Japan

Volume

43

Issue

9

fYear

1996

fDate

9/1/1996 12:00:00 AM

Firstpage

815

Lastpage

816

Abstract

Recently, Pyragas [1993] proposed a control method called delayed feedback control to stabilize unstable periodic orbits in nonlinear continuous-time systems. In this letter, we consider delayed state-feedback control in discrete-time systems. We show that a fixed point can not be stabilized by the delayed state-feedback control if the linearized system around the fixed point has an odd number of real eigenvalues greater than one. Moreover, in one- and two-dimensional systems, we show necessary and sufficient conditions for the local stabilization by the delayed state-feedback control

Keywords

delay systems; discrete time systems; eigenvalues and eigenfunctions; nonlinear control systems; stability; state feedback; delayed feedback control; linearized system; local stabilization; nonlinear discrete-time systems; one-dimensional systems; real eigenvalues; state-feedback control; two-dimensional systems; unstable periodic orbits; Chaos; Control systems; Delay; Eigenvalues and eigenfunctions; Feedback control; Force control; Nonlinear control systems; Orbits; Output feedback; Sufficient conditions;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.536757

Filename

536757