A dimension-reduced sliding mode control approach for fuzzy parameter-varying systems

Fuzzy parameter-varying (FPV) systems constitute an emerging framework for analyzing nonlinear systems. However, due to the coexistence of fuzzy logic and time-varying parameters, the stabilization methods for FPV systems often suffer from severe conservatism. To address this issue, this study proposes a dimension-reduced design method to construct an FPV sliding mode control (SMC) law for general FPV systems. Furthermore, the global asymptotic stability of the resulting control system is rigorously proved by the stability theory of switching systems. Finally, two simulation cases of different dimensions demonstrate the superiority of the proposed method in terms of stability and computational complexity.