Global K-exponential Stabilization of Non-symmetrical Underactuated Surface Vessels

A switching control law is proposed to control the non symmetrical underactuated surface vessel with non-integrable second-order nonholonomic constraints. First, global invertible transformations are used to transform the kinematics and dynamics of the vessel into two subsystems. Then, a Lyapunov like function is used to constructed an invariant set based on which the switching control law is designed. This control law guarantees global exponential convergence rates and global asymptotical stability, that is, the global K-exponential stability. The simulation results verifies the effectiveness.