This paper addresses the robust distributed fuzzy model predictive control (RDFMPC) problem for nonlinear systems subject to disturbance and coupled states. Initially, nonlinear subsystems are reformulated as Takagi-Sugeno (T-S) fuzzy models via sector nonlinearity. A distributed optimization problem is subsequently established over a finite horizon, employing a dual-mode approach with a synchronous update strategy. Within this framework, local control laws and terminal sets, comprising positive definite matrices and a terminal index incorporating performance and coupled state constraints, are derived using a vertex envelope optimization algorithm. Additionally, an interval predictor is developed by analyzing both the positive and negative mappings of the fuzzy system matrices. This predictor enables the reformulation of the RDFMPC optimization problem, significantly reducing the computational complexity associated with unpredictable membership functions (MFs) while enhancing system robustness against disturbances. The proposed algorithm is rigorously validated through its application to a three-cart-spring-damper system, demonstrating its practical effectiveness and superior performance.
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