This paper presents a novel state-feedback robust sliding-mode controller (SFRSMC) based on a mixed \(H_2/H_{\infty }\) approach to enhance the control performance of hydraulic turbine governing systems (HTGS) with complex conduit systems under external load disturbances and control signal uncertainties. A state-space model incorporating the dynamic responses of the HTGS is developed. The SFRSMC is designed using the sliding-mode equivalent control principle, with a disturbance observer to estimate and mitigate unknown disturbances. To balance robustness and optimality, mixed \(H_2/H_{\infty }\) linear matrix inequalities (LMIs) are utilized to determine the critical performance sliding matrix via an auxiliary feedback control method. The effectiveness of the proposed control scheme is validated through time-domain simulations under various operating scenarios, including different parameter variations of the HTGS.
