The \(H_{\infty }\) control of singular time-delay systems (STDs) with proportional-differential (PD) feedback of partial states is the main topic of this work. A new PD feedback controller with partial states is constructed, and the admissibility and \(H_{\infty }\) control problems are studied by figuring out the differential-algebraic equations of a class of STDs with external disturbances. Additionally, robust admissibility and robust admissibilization conditions are derived, allowing for the reduction of conservatism and the improvement of control impact with reduced computation. The utilization of a more concise controller in this study facilitates further reduction of decision variables compared to previous studies, while effectively striking a balance between conservatism, the quantity of decision variables, and control efficacy. Lastly, a few numerical examples illustrate the aforementioned claims.
