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An Approach for Robust Controller Design Based on a Remodeled Uncertain T–S Fuzzy Model With Nonparallel Distributed Compensation and a Fuzzy Lyapunov Function
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DOI：10.1109/tfuzz.2026.3698848.png)
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Abstract
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This study provides a modeling framework for representing uncertain nonlinear systems using a remodeled uncertain Takagi–Sugeno (T–S) fuzzy model. The stability of the uncertain T–S fuzzy model is addressed through a novel approach that simultaneously handles uncertainties in both the premise and consequent parts. First, a fuzzy basis transformation is introduced to demonstrate the existence of a corresponding representation at different operating points. Based on this concept, an approximate T–S fuzzy model with a common consequent basis is derived to capture predefined uncertainties. Consequently, a reformulated T–S fuzzy model at a fixed operating point is constructed to facilitate controller design. By overcoming the convex-sum property of the traditional T–S fuzzy model, the remodeled system achieves more flexible design and avoids uncertainties in the consequent part. To handle the possibility that membership functions may become negative, normalized membership functions at the design point are introduced to ensure the necessary conditions for stability analysis. The controller is formulated using a fuzzy Lyapunov function and nonparallel distributed compensation to balance robustness and conservatism. Finally, the effectiveness of the proposed approach is demonstrated through two benchmark examples: a mass–spring–damper system and a flexible joint robot subject to uncertainties.
Keywords:
Fuzzy basis transformation (FBT)
Fuzzy lyapunov function
nonparallel distributed compensation (NPDC)
uncertain Takagi–Sugeno (T–S) fuzzy system
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11.9
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