Remarks on the stabilizability of integrator switching systems

In this work, a class of switching systems known as integrator is studied. Such systems have the feature of being very simple and allow us to gain insight on the effect that the switching sequence has on system stability. Three problems are analyzed. First, the practical stabilizability problem under system uncertainty is studied. Confinement regions are explicitly computed, and switching sequences based on the nominal behavior of the systems are derived. Second, the practical stabilizability problem using output feedback is solved; in this case, sufficient conditions are proposed. Finally, by joining both results, sufficient conditions for practical stabilizability of uncertain systems under output feedback are given. The results are illustrated with examples and some extensions for uncertain linear system and event-based switching are given.