This paper presents a new active control strategy with enhanced robustness for the structural systems with nonlinear uncertainties and exogenous disturbances. Particularly, due to existence of the perturbation in the mass matrix, the considered plant is described by a dynamical model with neural uncertainty, or an uncertain descriptor (or singular) system. A novel direct robust vibration control law is then provided in terms of algebraic solutions based on linear matrix inequality, where the robustness against the modelling and parametric perturbations, controller variations and disturbance excitations can be guaranteed simultaneously. A numeral example is provided to show the efficiency of the approach.