Further results on global stabilisation and tracking control for underactuated surface vessels with non-diagonal inertia and damping matrices

This paper studies the global uniform stabilisation and exponential tracking problems for an underactuated ship with non-diagonal inertia and damping matrices. For the synthesis of the controller, first, the underactuated ship in question is converted into two cascade connected subsystems by using state and input transformations. Two constructive backstepping design schemes are developed, respectively, to get around the stabilisation burden and tracking burden. Along the way of proving stability analysis, it is shown that the designed control strategies can guarantee the global uniform asymptotic convergence of the state to the origin and global exponential convergence to the desired reference trajectory. Simulation results are provided to demonstrate the effectiveness of the proposed control methodologies.