Stability analysis of discontinuous dynamical systems using vector Lyapunov functions

In this paper, we establish several stability results for discontinuous dynamical systems defined onR ⁺=0, ) which make use of vector Lyapunov functions. For the scalar case, these results yield in particular theprincipal Lyapunov stability results for discontinuous dynamical systems reported earlier. We demonstrate the applicability of our results by studying a class of interconnected discontinuous dynamical systems and several specific examples.This research was supported in part by an Alexander von Humboldt Foundation Senior Research Award, Institut für Nachrichtentechnik, Ruhr-Universität Bochum, Germany, and by a Center of Applied Mathematics Fellowship, University of Notre Dame.