Feedback stabilization of steady-state and Hopf bifurcations

Author

Wang, Yong ; Murray, Richard M.

Author_Institution

Div. of Eng. & Appl. Sci., California Inst. of Technol., Pasadena, CA, USA

Volume

3

fYear

1998

fDate

1998

Firstpage

2431

Abstract

We consider nonlinear systems with steady-state or Hopf bifurcations for which the bifurcated modes are linearly unstabilizable. The goal is to find sufficiently smooth state feedbacks such that the bifurcation for the closed loop system is supercritical, and at the same time, the linearly controllable subsystem is asymptotically stable. We solve this problem by giving necessary and sufficient conditions under the assumption that certain nondegeneracy conditions are satisfied. We also give explicit construction of stabilizing feedbacks and illustrate the theory using simple examples

Keywords

asymptotic stability; bifurcation; closed loop systems; nonlinear control systems; state feedback; Hopf bifurcations; asymptotic stability; closed loop system; feedback stabilization; linearly controllable subsystem; linearly unstabilizable modes; necessary and sufficient conditions; nondegeneracy conditions; nonlinear systems; state feedbacks; steady-state bifurcations; Bifurcation; Closed loop systems; Control systems; Eigenvalues and eigenfunctions; Feedback loop; Linear feedback control systems; Nonlinear systems; State feedback; Steady-state; Sufficient conditions;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1998. Proceedings of the 37th IEEE Conference on

Conference_Location

Tampa, FL

ISSN

0191-2216

Print_ISBN

0-7803-4394-8

Type

conf

DOI

10.1109/CDC.1998.757773

Filename

757773