Global Stabilization of A Class of Nonholonomic Integrators via Discontinuous Control

This paper investigates the discontinuous state feedback control for stabilizing a class of nonholonomic integrators with drift terms.The control design relies on constraining state trajectory in an invariant set.To this end, we apply constant controls to drive the states moving into the invariant set and then switch to a continuous control law with suitable gain selections.It is proven in the Lyapunov sense that the proposed control scheme achieves global exponential stabilization of the states, and the control switch would only occur at most once.Numerical simulations are carried out to validate the proposed control law.