This paper presents a robust H∞ output feedback control approach for structural systems with uncertainties in model parameters by using available acceleration measurements and proposes conditions for the existence of such a robust output feedback controller. The uncertainties of structural stiffness, damping and mass parameters are assumed to be norm-bounded. The proposed control approach is formulated within the framework of linear matrix inequalities, for which existing convex optimization techniques, such as the LMI toolbox in MATLAB, can be used effectively and conveniently. To illustrate the effectiveness of the proposed robust H∞ strategy, a six-story building was subjected both to the 1940 El Centro earthquake record and to a suddenly applied Kanai-Tajimi filtered white noise random excitation. The results show that the proposed robust H∞ controller provides satisfactory results with or without variation of the structural stiffness, damping and mass parameters. This paper presents a robust H∞ output feedback control approach for structural systems with uncertainties in model parameters by using available acceleration measurements and Viking conditions for the existence of such a robust output feedback controller. The uncertainties of structural stiffness, damping and mass parameters are as to be norm-bounded. The proposed control approach is formulated within the framework of linear matrix inequalities, for which existing convex optimization techniques, such as the LMI toolbox in MATLAB, can be used effectively and conveniently. H∞ strategy, a six-story building was imposed both on the 1940 El Centro earthquake record and to a suddenly applied Kanai-Tajimi filtered white noise random excitation. The results show that proposed robust H∞ controller provides satisfactory results with or without variation of the structural stiffness, damping and mass parameters.