Local Robustness of Bifurcation Stabilization with Applications to Jet Engine Control

Local robustness of bifurcation stabilization is studied for parameterized nonlinear systems of which the linearized system possesses either a simple zero eigenvalue or a pair of imaginary eigenvalues and the bifurcated solution is unstable at the critical value of the parameter. It is assumed that the unstable mode corresponding to the critical eigenvalue of the linearized system is not linearly controllable by the feedback control, nor linearly affected by the uncertainty signal. Computable conditions are derived to characterize the admissible uncertainty sets for systems with pitchfork, transcritical and Hopf bifurcations. The result for stationary bifurcation is applied to analyzing the robustness of several static stabilizing control laws for axial-flow compressors based on the approximated third-order Moore-Greitzer model.