Global asymptotic stabilization of underactuated surface vessels with nonzero off-diagonal terms in their system matrices

This paper considers the global asymptotic stability controller for a class of asymmetric underactuated surface vessel. Different from the most existing results, we construct a new time-varying stabilizer such that the origin is a solution of the closed-loop system. For the synthesis of controller, the investigated underactuated model is converted into two cascade connected subsystems using input and state transformations. For these subsystems, it is shown that the stabilization problem of this note can be reduced to the one of the second subsystem. By combining the direct Lyapunov method and nonlinear time-varying tools, a time-varying stabilization controller is developed guaranteeing global uniform convergence of the full states to origin. The simulation results testify to the effectiveness of the presented control approach.