Neural networks are approximation techniques that can be characterized by adaptability rather than by precision. For feedback systems, high precision can still be acquired in presence of errors. Within a general iterative framework of closed-loop kinematic robotic control using linear local modeling, the inverse Jacobian matrix error and the maximum length of the displacement for which the linear model is valid are computed. They guarantee convergence of the feedback loop. The error bounds are computed for our manipulator. The theoretical results are validated by simulation.