What form of control function can drive a discontinuous-mode boost converter to chaos via period-doubling?

Period-doubling routes to chaos in dc/dc converters operating in discontinuous mode have been reported in Reference 1 for the boost-type converter, and in Reference 2 for the buck-type converter. The chaotic behaviour associated with such systems is due to the presence of the feedback controller since these systems are open-loop stable.3 Thus, the choice of the feedback control function is very important to the identi cation and control of chaos in such systems. Up to now, no rigorous attempts have been made to derive formally the condition leading to chaos in such systems. In this letter we establish condition on the form of control function that may give rise to period-doubling cascades in the boost regulator operating in discontinuous mode. In Reference 1 a closed-form iterative map that describes the dynamics of the boost regulator operating in discontinuous mode has been derived. Using this map, period-doubling cascades have been predicted when the regulator is controlled under a simple proportional feedback, the bifurcation parameter being the feedback gain. Experimental measurement bears witness to the predicted chaos.1 Although the work op. cit. gives no theoretical insights into the underlying cause of chaos in such systems, it does prompt the important practical question of what form of feedback control may give rise to chaotic behaviour. This letter attempts to answer this question in the light of the Schwarzian derivative. The system under study is periodically driven with period T , and is in general described by a rst-order iterative map of the form: