LINEAR FEEDBACK STABILIZATION OF NONLINEAR-SYSTEMS WITH AN UNCONTROLLABLE CRITICAL MODE

Linear feedback stabilization of nonlinear systems is studied for syst ems whose linearization at an equilibrium point possesses a simple cri tical mode that is uncontrollable. The results complement previous wor k on the synthesis of nonlinear stabilizing control laws. The present work addresses continuous-time systems for which the linearization has either a simple zero eigenvalue or a pair of simple pure imaginary ei genvalues. Both the stability analysis and stabilizing control design employ results on stability of bifurcations of parameterized systems.