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In this work, we investigate the state stabilization and trajectory trackingproblems of underactuated surface ships with full state model of havingnon-diagonal inertia and damping matrices. By combining the novel statetransformations, the direct Lyapunov approach, and the nonlinear time-varyingtools, the stabilization and the trajectory tracking controllers are developedrespectively guaranteeing global uniform asymptotic convergence of the state tothe desired set point and global exponential convergence to the desiredreference trajectory via mild persistent exciting conditions. Simulationexamples are given to illustrate the effectiveness of the proposed controlschemes.

Global uniform asymptotic stabilization and k-exponential trajectory  tracking of underactuated surface ships with non-diagonal inertia/damping  matrices