Control of Hopf bifurcations of nonlinear infinite-dimensional systems: application to axial flow engine compressor

Abstract

We study the local feedback stabilization of Hopf bifurcations for nonlinear systems of infinite dimensions in the case where the linearized vector field has a pair of simple nonzero imaginary eigenvalues and all its other eigenvalues lie strictly in the left half-plane. Discussing the normal form of nonlinear systems obtained by making use of the integral averaging method, we obtain sufficient and necessary condition for controlling the stability of the systems even if the critical modes are uncontrollable. As an application, we apply the obtained results to the control of axial flow engine compressor.

Keywords:

• nonlinear systems
• infinite-dimensional spaces
• Hopf bifurcation
• integral averaging
• stabilization

AMS Subject Classifications:

• 93D15
• 35K55

Acknowledgement

This research is supported in part by the Natural Science Foundation of Guangdong Province 8151009001000044, in part by NSF 1021203 of the United States.