In web transport systems, the main concern is to control independently speed and tension in spite of perturbations, such as radius variations and changes of set points. In this paper we present multivariable H_infin controllers, applied to winding systems and determined by a bilinear matrix inequality (BMI) approach. The design relies on full state feedback, with or without addition of integrators. The use of partial integral action for error-free reference tracking and disturbance rejection is established theoretically and discussed in this paper. Simulation results are given based on a nonlinear model identified on a 3-motor winding test bench as well as on its 9-motor expansion