  In this work, we investigate the state stabilization and trajectory tracking
problems of underactuated surface ships with full state model of having
non-diagonal inertia and damping matrices. By combining the novel state
transformations, the direct Lyapunov approach, and the nonlinear time-varying
tools, the stabilization and the trajectory tracking controllers are developed
respectively guaranteeing global uniform asymptotic convergence of the state to
the desired set point and global exponential convergence to the desired
reference trajectory via mild persistent exciting conditions. Simulation
examples are given to illustrate the effectiveness of the proposed control
schemes.
