Global κκ-exponential asymptotic stabilization of underactuated surface vessels

In this work, a time-invariant switching control law is proposed to make the desired set point of an underactuated surface vessel globally asymptotically stable with exponential convergence rate (κκ-exponential stable). The construction of the controller relies on discontinuous coordinate/input transformations and a Lyapunov-like switching function. The result is the first stabilizing law able to achieve global κκ-exponential stability of the underactuated surface vessel. The effectiveness of the proposed control law is verified by simulation.