LMI for stability and robustness of hybrid systems

This paper presents results for stability and robustness of hybrid systems consisting of nonlinear subsystems. Present stability results that are extensions of classical Lyapunov theory are restricted to certain kinds of hybrid systems. For example, it is required that all subsystems have the same equilibrium point. In this paper these results are generalized, but more importantly, it is shown how Lyapunov functions for hybrid systems can be solved by linear matrix inequalities (LMI). Furthermore, it is shown how uncertainties around the nominal switch sets can be handled by introducing acceptable switch regions as additional stability conditions. The theory is illustrated by an example.