The development of feedback control systems for overhead cranes is of great importance due to many potential applications and advantages over manual operation concerning stability and robustness. We represent the key nonlinear dynamics of cranes in a compact state-space fuzzy model. The fuzzy model assists the design of a fuzzy controller through parallel distributed compensation. A conservative linear-matrix-inequality feasibility problem is formulated so that a solution guarantees closed-loop Lyapunov stability, constrained inputs, quick positioning of the supporting cart and suppression of load oscillations. Due to the nonlinear nature of the fuzzy model and controller, Jacobian linearization at a hyperbolic equilibrium is avoided. The proposed fuzzy controller for cranes has shown to be effective, robust and able to move loads smoothly even after collisions. Constrained and smooth inputs avoid actuator saturation and tend to increase its lifetime.