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The paper shows that a large class of underactuated vehicles cannot be asymptotically stabilized by either continuous nor discontinuous state feedback. Furthermore, stabilization of an underactuated surface vessel is considered. Controllability properties of the surface vessel is presented, and a continuous periodic time-varying feedback law is proposed. It is shown that this feedback law exponentially stabilizes the surface vessel to the origin, and this is illustrated by simulations.
Pettersen et al. (Tue,) studied this question.