Optimal static output feedback (OSOF) control is used to obtain the control force desired from a magnetorheological (MR) damper fitted between ground and first storey of a three-storey building model. The modified Bouc–Wen model is considered for obtaining damper response. This exhibits a non-linear relationship between damper force and input-voltage/states, and hence obtaining the input voltage to realize a desired control force is a non-trivial task. Two voltage control laws are proposed, i.e. inverse quadratic voltage law (IQVL) and inverse On–off voltage law (IOOVL), both based on the MR constraint filter. These are implemented in addition to the existing clipped voltage law (CVL). Results for controlled response of the building are obtained in terms of peak and RMS values of response quantities (Interstorey Drift, Displacement, Acceleration). These are compared with existing results obtained via linear quadratic Gaussian (LQG) control using CVL, and via passive-on control with constant (saturation) voltage applied. A reduction in the maximum peak interstorey drift, maximum RMS interstorey drift, and performance index is obtained when using OSOF-IOOVL/CVL control as compared with passive-on control. These quantities as well as RMS storey displacements are attenuated when comparing OSOF-IOOVL/CVL control with LQG-CVL control, with the exception of maximum peak interstorey drift for which the attenuation occurs for IOOVL only. The peak and RMS values of accelerations are reduced via OSOF compared with passive-on/LQG-CVL control, except when considering first-storey accelerations using passive-on control. The peak value of the applied damper force is least when using OSOF control. Copyright © 2010 John Wiley & Sons, Ltd.