This paper presents a new switching anti-windup compensation design to maximize the domain of attraction for a supercavitating vehicle subject to actuator saturation. The dive-plane dynamics of the vehicle are considered. By applying the linear differential inclusion expression of saturated feedbacks, conditions under which the compensator locally stabilizes the closed-loop system are then derived. The design of anti-windup gains on maximizing the system's domain of attraction is finally formulated and solved as an iterative optimization problem with linear matrix inequality (LMI) constraints. Simulations are conducted for systems with magnitude and rate limits to evaluate the effectiveness of the proposed method.