Homogeneous stabilization of the extended chained form system

A controller is presented for point stabilization of the extended chained form system. The extended chained form system can not be stabilized by means of continuous pure-state feedback. Moreover, it can not be exponentially stabilized by smooth feedback, since the linearization around equilibrium points is uncontrollable. In this paper, a controller is given that ρ-exponentially stabilizes the system. The controller is derived by using a combined averaging technique for homogeneous systems and a backstepping approach. The controller is illustrated in a benchmark example by application to the V/STOL aircraft without gravity