This paper considers some control design problems in a power system driven by battery/supercapacitor hybrid energy storage devices. The currents in the battery and the supercapacitor are actively controlled by two bidirectional buck–boost converters. Two control objectives are addressed in this paper: one is to achieve robust tracking of two reference variables, the battery current and the load voltage, the other is to achieve smooth transition of these variables during load switch. Based on the state-space averaged model we newly developed, the control design problems are converted into numerically efficient optimization problems with linear matrix inequality (LMI) constraints. An experimental system is constructed to validate the control design methods.