Discrete-time modeling and analysis of pulse-width-modulated switched power converters

The subject of this paper is a general theory for a switched power converter, where the switch is controlled according to a pulse-width-modulation strategy. The pulse-width-modulated switched power converter is transformed into an equivalent discrete-time system. With this system the existence, uniqueness and stability of stationary solutions is investigated. Also stability of deviations from a stationary solution is investigated. Furthermore, feedback control situations are considered. It is shown that two kinds of modulators, namely the running and fixed modulator, may invoke a very different behaviour of the feedback control system. The phenomenon of subharmonic oscillations is shown to be a special case of the normal unstable behaviour.