This paper investigates the control problem of a highly nonlinear double-pendulum overhead crane (DPOC) system. In industrial applications, such cranes are typically modeled as a trolley coupled with a double pendulum, where strong nonlinear couplings and underactuated dynamics make controller design a challenging task. To effectively handle these nonlinearities, a reduced-complexity Takagi–Sugeno fuzzy descriptor (RC-TSFD) model is proposed, which accurately represents the nonlinear behavior of the system using a limited number of linear submodels. Based on this modeling framework, a Linear Matrix Inequality (LMI)-based state-feedback control scheme is developed to ensure closed-loop stability and disturbance attenuation according to Lyapunov stability theory. The proposed method significantly reduces the computational burden associated with the conventional Takagi–Sugeno fuzzy descriptor (TSFD) approach, while maintaining comparable control performance and robustness. Simulation studies demonstrate that the proposed control scheme achieves precise trolley movement and swing reduction, confirming both high efficiency and robustness for the DPOC system.
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