On the Stabilisation of Switching Electrical Power Converters

This paper considers the control of switching power converters which are a particular class of hybrid systems. Such systems, which are controlled by switches, can be modeled using physical principles. Taking advantage of the energetical properties of their models, a Lyapunov function is proposed. This function, which has not to be computed but is systematically deduced from the physical model, allows to derive different stabilizing switching sequences. From a theoretical point of view, asymptotic stability can be obtained, but it requires null intervals between switching times. In order to ensure a minimum time between switchings, this Lyapunov function has to be increasing for a small duration by using a delay or a dead zone. A control law principle that guarantees the invariance of a specified domain with respect to state trajectories is proposed. Two examples are provided at the end of this paper that demonstrate the efficiency of the proposed approach.