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This note considers the stabilization problem of an underactuated surface vessel. Three global smooth time-varying control laws are proposed with the aid of different techniques. The first proposed control law makes the state of the closed-loop system asymptotically converge to zero, while the second and the third control laws make the state of the closed-loop system globally exponentially converge to zero. Moreover, the exponential convergence rate of the state of the closed-loop system can be arbitrarily assigned with the third control law. Simulation results show that the proposed control laws are effective.
Dong et al. (2005) studied this question.