Hybrid impulsive control for global stabilization of subfully actuated systems

This paper presents the first study of the global stabilization of subfully actuated systems (sub-FAS) by hybrid impulsive control method. Since sub-FAS contain singular sets, controllers designed by the conventional high-order fully actuated (HOFA) system approach may not be feasible for all initial conditions in the state space. Different from existing studies that constrain initial conditions to achieve substabilization, we devise a hybrid controller via the HOFA system approach and state-dependent impulsive control method, addressing the global stabilization problem without constraints on the initial states. By transforming sub-FAS into hybrid systems through the hybrid controller, we obtain some criteria for global stabilization of the sub-FAS. It is noted that both stabilizing and destabilizing impulses are used to overcome the singular sets in the sub-FAS. Finally, two examples illustrate the proposed approach.