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This paper proposes a supervisory interval type-2 Tagaki-Sugeno-Kang neural fuzzy network (IT2TSKNFN) control system for precision motion control of linear microstepping motor (LMSM) drives. The IT2TSKNFN incorporates interval type-2 fuzzy sets and TSK fuzzy reasoning into an NFN to handle uncertainties in LMSM drives, including payload variation, external disturbance, and sense noise. Based on the IT2TSKNFN, an uncertainty observer is first introduced to watch compound system uncertainties. Subsequently, an IT2TSKNFN-based controller is developed with robust hybrid control scheme, in which H∞ approach and a supervisory controller are embedded to overcome the effects of unstructured uncertainties and reconstruction errors. The supervisory controller combines variable structure control and adaptive IT2TSKNFN control with different weights based on the tracking error. Moreover, projection-type adaptive algorithms that can tune parameters of the IT2TSKNFN online are derived from the Lyapunov synthesis approach; thus, the stability and robustness of the overall control system are guaranteed. Finally, the proposed control algorithms are realized within a TMS320VC33 DSP-based control computer. Simulated and experimental results of an LMSM drive are provided to verify the effectiveness of the proposed IT2TSKNFN control system.