In this paper digital optimal control of pulse-width-modulated switched linear systems is considered. The equivalent discrete-time system and its deviation around a stationary solution plays an important role. An optimal linear discrete-time deviation controller is developed. The controller is chosen to be one-step-ahead predictive, which is a natural choice for control of digital pulse-modulated systems. The controller is optimal, i.e. a cost criterion is minimized. The theory is generally applicable and gives, in principle, a tool to design a digital optimal controller for an arbitrary pulse-width-modulated switched linear system. The theory is illustrated by examples from the field of switched electrical networks. (C) 2003 Elsevier Ltd. All rights reserved.