Boolean Sliding Mode Control of Multilevel Power Converters

A generic method to build Boolean sliding mode controllers for switching systems, addressed by a previous contribution, basically formulates the synthesis problem as a set of linear matrix inequalities (LMI) defining the parameters of commutation hyperplanes which all intersect on a prescribed sliding manifold. Yet it cannot guarantee the existence of a sliding motion from any initial condition, since it only ensures a local attractivity of the sliding manifold with respect to state trajectories. Aiming at improving this method, the present paper introduces some additional LMI constraints, which eliminate from the admissible solutions the sets of commutation hyperplanes that some state trajectories possibly never intersect. Algorithmic aspects are also considered for the resolution. The efficiency of the step is illustrated by its application to a multilevel power converter.