Abstract— Efficient control of liquid level – in a carbonization column (CCl) of soda ash production plants – is a difficult task because the plants are nonlinear, subjected to disturbances and lack a reliable mathematical model. To attain such efficient control, model-free fuzzy logic controllers (FLC) based on empirical knowledge are successfully developed and implemented, and adaptation mechanisms are added to aid the FLC tuning and compensate for plant changes. However, the stability analysis – of the adaptive FLC (AFLC) systems – is a critical issue that needs addressing. For this reason, the current investigation is devoted to the development of a method for analyzing AFLC system stability using robust stability and robust performance criteria. The suggested method is employed for the stability analysis of a designed PID AFLC utilized for liquid level control in an industrial CCl. The obtained results reveal that the AFLC preserves stability and high system performance in the whole range of adaptation and considered changes of the plant and the operation conditions. Moreover, the results unveil that the developed method can also be applied for the design of a robust FLC system that competes with adaptive counterparts.