Bifurcation stabilization with local output feedback

Local output feedback stabilization with smooth nonlinear controllers is st udied for parameterized nonlinear systems for which the linearized system p ossesses either a simple zero eigenvalue or a pair of imaginary eigenvalues and the bifurcated solution is unstable at the critical value of the param eter. It is assumed that the unstable mode corresponding to the critical ei genvalue of the linearized system is not linearly controllable. Results are established for bifurcation stabilization using output feedback where the critical mode can be either linearly observable or linearly unobservable. T he stabilizability conditions are characterized in explicit forms that can be used to synthesize stabilizing controllers. The results obtained in this paper are applied to rotating stall control for axial flow compressors as an application example.