Overhead cranes are widely used structures for lifting and conveying heavy loads. The development of feedback control systems for such equipment is important due to the large number of potential applications and advantages over manual operation concerning stability and robustness. This paper aims to represent the key nonlinear dynamics of crane systems by means of a state-space fuzzy model with compact rule-base structure. The fuzzy model is useful to assist the design of a fuzzy controller based on the concept of parallel compensation. A well-posed conservative linear-matrix-inequality (LMI) feasibility problem is formulated so that a solution guarantees closed-loop Lyapunov stability, bounded control inputs, quick positioning of the supporting cart, and suppression of load oscillations and collisions. The fuzzy controller is composed by rules with linear control laws derived from local state-space models. The controller warrants asymptotic convergence of the states. Due to the nonlinear nature of the fuzzy model and controller, Jacobian linearization is avoided. The proposed fuzzy control approach for cranes has shown to be more effective and robust than an optimal quadratic controller, and able to move cargo smoothly and safely to a destination. Particularly, constrained and smoother control inputs avoid actuator saturation, and tend to increase its lifetime. Laboratory experiments using the LMI fuzzy controller and actual data validates the approach for cranes in actual scenario.