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Stabilisation is an issue of great practical importance to the ship industry. This study considers the global asymptotic stability controller for a class of underactuated surface vessel possessing non-diagonal inertia and damping matrices. For the synthesis of controller, the investigated underactuated model is first converted into two cascade connected subsystems using input and state transformations. For these subsystems, it is shown that the stabilisation problem of this study can be reduced to the one of the second subsystem. By combining the method of adding a power integrator and the direct Lyapunov approach, a finite time switching control strategy is developed guaranteeing global asymptotic convergence of the full states to origin. The simulation results testify to the effectiveness of the presented control approach.

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This paper studies the problem of state-feedback stabilization control for a class of high order stochastic nonholonomic systems with disturbed virtual control directions and more general nonlinear drifts. By using the backstepping approach, we develop a recursive controller design procedure in the stochastic setting. To get around the stabilization burden associated with nonholonomic systems, a switching control strategy is exploited in this procedure. The tuning function technique is applied in the design to avoid the disadvantage of overparameterization. It is shown that, under some conditions, the designed controller could ensure that the closed-loop system is almost asymptotically stabilized in probability. It is noted that the obtained conclusion can be extended to multi-input systems. A simulation example is provided to illustrate the effectiveness of the proposed approach.

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