Generalized Fuzzy Hyperbolic Models (GFHMs) offer a simpler structure and less computational complexity than the typical fuzzy systems. Type-2 fuzzy systems, in contrast, have better handling of uncertainty but at the cost of higher computational complexity. Here, we propose a synergistic hybrid framework of interval type-2 fuzzy systems and GFHMs for a better uncertainty handling and simpler computational structure in the modelling and control of nonlinear systems. For this purpose, we first extend the GFHM to a computational model with various width and subsequently propose interval type-2 generalized fuzzy hyperbolic systems (IT2-GFHS) as a computational framework for nonlinear systems modelling. We then employ this IT2-GFHS in a general sliding-based robust nonlinear controller. Theoretical Lyapunov analysis reveals the overall asymptotic stability of the resulting closedloop system. The numerical simulations for system modelling and identification on two nonlinear benchmark problems also reveal higher accuracy, lower computation time, and fewer adjustable parameters for the proposed IT2-GFHS models. Furthermore, applications to two nonlinear benchmark control problems show similar performance in terms of robustness to noise and disturbances compared with type-2 fuzzy systems, with the IT2-GFHS-based nonlinear controller having considerably fewer computations and floating-point operations. Finally, the proposed approach is experimentally implemented to control a 3-Prismatic-Series-Prismatic (3-PSP) parallel robot. Experimental results also confirm the improved tracking performance of the proposed method compared with interval type-2 and type-1 fuzzy systems, while also requiring fewer adjustable parameters.

Keywords