Autonomy of underwater vehicles has become an imperative feature due to increasingly challenging deep sea mission scenarios. In particular, for trajectory-tracking problems of Autonomous Underwater Vehicles (AUVs), the use of Lyapunov theory tools in state-of-the-art methods is common practice. These often require special assumptions, according to the application considered, and ‘intuition’ for the choice of a control law, which often leads to conservative results. This article suggests a systematic analysis for the horizontal motion of an AUV which ensures global asymptotic stability for the closed loop system. A nonlinear underactuated AUV system is considered with linear and angular velocity constraints. The Takagi–Sugeno (TS) framework design is adopted for the representation of the original nonlinear system. The control law is synthesised using the standard parallel distributed compensation (PDC) control law structure and stability is guaranteed for the closed loop system. The design criteria are posed as linear matrix inequalities (LMIs) where sufficient conditions for the design of the control law are shown. The proposed approach can be easily adopted for different types of autonomous vehicles with minor modifications.