The Controlled Center Systems

In this correspondence, we propose a methodology to stabilize systems with control bifurcations by introducing ldquothe controlled center systems.rdquo A controlled center system is a reduced-order controlled dynamics consisting of the linearly uncontrollable dynamics with the first variable of the linearly controllable dynamics as input. The controller of the full order system is then constructed. We apply this methodology to systems with a transcontrollable, a Hopf, and a double-zero, control bifurcation.