Switching control for a class of sub-fully actuated systems

This paper studied stability of a class of sub-fully actuated systems under the framework of high-order fully-actuated system approach. The under-actuated set is described by a hyperplane. A switching control law is designed for the sub-fully actuated system, where the control input equals to zero when the state trajectory is in the neighborhood of the under-actuated set; and the control input is designed the same as fully-actuated case otherwise. Under certain conditions, the state trajectory of the closed-loop system will cross the under-actuated hyperplane and converge to the origin exponentially.