Designing the control strategy for a flexible robotic arm has long been considered a complex problem as it requires stabilizing the vibration simultaneously with the primary objective of position control. A stable state-feedback fuzzy controller is proposed here for such a flexible arm. The controller is designed on the basis of a neuro-fuzzy state-space model that is successfully trained using the experimental data acquired from a real robotic arm. The complex problem of solving stability conditions is taken care of by recasting them in the form of linear matrix inequalities and then solving them using a popular interior-point-based method. This asymptotically stable fuzzy controller is further augmented to provide enhanced transient performance along with maintaining the excellent steady-state performance shown by the stable control strategy. The controller hence designed has been successfully implemented for a real robotic arm to operate over a long angular range of 180 with several payload conditions and, for situations where the system is operated for a long range and with a large variation in payload conditions, it could successfully outperform the recently proposed proportional derivative and strain controller.