The paper deals with the robust non-fragile H∞ control problem for uncertain structural systems with additive controller gain variations. The parameter uncertainties for the mass, damping and stiffness of the structural systems are unknown but norm bounded. Based on the H ∞. control theory and a linear matrix inequality formulation, a new method for designing a robust state-feedback control law is presented. The objective is to reduce the disturbance on the controlled output to a prescribed level for all admissible parametric uncertainties and controller gain variations. A four-degree-of-freedom building model subject to seismic excitation is used to illustrate the effectiveness of the approach through simulation. © 2003 Elsevier Ltd. All rights reserved.