Title :
Feedback control of Hopf bifurcations via integral averaging method
Author :
Xiao, MingQing ; Kang, Wei
Author_Institution :
Dept. of Math., Southern Illinois Univ., Carbondale, IL, USA
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. Through discussing the normal form of nonlinear systems obtained by the integral averaging method, we discuss some conditions for controlling the stability of the systems, provided that the critical modes are uncontrollable. As an example, we apply the obtained results to the control of axial flow compressor model
Keywords :
bifurcation; eigenvalues and eigenfunctions; feedback; multidimensional systems; nonlinear control systems; stability; Hopf bifurcations; axial flow compressor model; feedback control; infinite-dimensional systems; integral averaging method; linearized vector field; local feedback stabilization; nonlinear systems; nonzero imaginary eigenvalues; stability; uncontrollable critical modes; Bifurcation; Control systems; Controllability; Eigenvalues and eigenfunctions; Feedback control; Linear feedback control systems; Mathematics; Nonlinear control systems; Nonlinear systems; Stability;
Conference_Titel :
Decision and Control, 2000. Proceedings of the 39th IEEE Conference on
Conference_Location :
Sydney, NSW
Print_ISBN :
0-7803-6638-7
DOI :
10.1109/CDC.2000.914098
