This paper addresses on a horizontal waypoint tracking problem for a class of nonlinear autonomous underwater vehicles (AUVs) with actuator saturations while keeping its constant surge speed. The concerned problem is formulated as an exponential stabilization of the error dynamics with respect to the desired surge speed and the desired yaw angle determined from the line of sight. It is shown that the feedback linearization technique makes the separate design of the available control inputs, the propeller thrust and the rudder angle, possible. By using the sector nonlinearity, the error dynamics is modeled as a polytopic linear parameter varying (LPV) system. Then, sufficient linear matrix inequality (LMI) conditions for its regional exponential stabilizability are derived in the sense of Lyapunov stability criterion. An example is provided to illustrate the effectiveness of the proposed methodology. (C) 2015 Elsevier Ltd. All rights reserved.