The Online Neuro-Fuzzy Controller (ONFC) is a fuzzy-based adaptive control that uses a very simple structure and can control nonlinear, time-varying and uncertain systems. Its efficiency and low computational cost allowed applications in several industrial plants successfully. However, none of the previous works on the ONFC provided a design procedure endowed with formal guarantees of robust closed-loop stability. In this paper, some conditions for ONFC robust stability, considering system polytopic uncertainties, are presented using the Lyapunov method. A new adaptation rule is proposed that dynamically varies the adaptation gain and incorporates the dead-zone technique to ensure robustness to the noise measurement. A reference model is also introduced, in order to allow a direct specification of the closedloop dynamics. Simulation results show that the new design conditions present good performance in the control of several types of systems. INDEX TERMS Adaptive control, fuzzy control, ONFC, robust stability.