Robust control of a class of switched dynamical systems is considered. The switching is controlled by pulse-width modulation (PWM). This idea is used, for example, in power electronics for power conversion. The class of systems considered includes digitally controlled power converters of many different types. The traditional approach to control design for power converters rely on an averaged model that ignores the high frequency behavior and the inherent time delay due to sampling. In contrast, the method presented here is based on a sampled-data model which takes the switched nature of the system into account. The sampled-data model is approximated by a linear quadratic model to which sampled-data H∞theory can be extended. The approach is applied to a bidirectional boost converter which is subjected to a large load disturbance.