This paper presents a sample control design for the base-isolated benchmark building with bilinear hysteretic bearings (e.g. lead-rubber bearings). Since there is no well-defined control strategy for nonlinear structures, and available linear strategies are well-known among the civil engineering community, a linear quadratic Gaussian (LQG) controller is selected for this purpose. To utilize an LQG controller, a linearized model of the nonlinear structure is required. A good linearized model, however, should be able to represent the nonlinear structure responses when both are controlled. It is shown that design problems of an equivalent linear model and an LQG controller are not, in fact, independent and require one for the other. In this study, the LQG controller is designed based on some parametric studies, and an iterative method is proposed for the development of an equivalent linear model. In the iterative method, the equivalent linear model is formed by replacing the nonlinear isolation elements that have bilinear stiffness and zero damping in the benchmark structure with a linear stiffness and a linear damping. Here, the linear stiffness is determined in the iterative method such that the RMS force of the bilinear isolation elements in the controlled (nonlinear) benchmark structure is equivalent to that of the corresponding isolation elements in the equivalent linear model. The overall approach is applied to the benchmark structure for seven historical earthquake ground acceleration data, and both an LQG controller and an equivalent linear model are obtained. The numerical simulations show that the equivalent linear model successfully replicates the nonlinear response, and the controller is able to improve the overall performance. As the final designs are not intended to be competitive, the method proposed can be improved in several ways to obtain better results. While the equivalent linear model developed herein may be used as a starting point in studying this benchmark problem, because of the strong interaction between controller and equivalent linear model, the participants of the base isolation benchmark problem are strongly encouraged to develop their own controller-specific equivalent linear models. Copyright (c) 2005 John Wiley & Sons, Ltd.