A comparison theory for stability analysis of discontinuous dynamical systems. II. Results involving vector Lyapunov functions

We establish several stability results for discontinuous dynamical systems defined on R⁺=[0,∞) which make use of vector Lyapunov functions. For the scalar case, these results yield in particular the principal Lyapunov stability results for discontinuous dynamical systems reported in part I (1998). We show how these results can also be employed in establishing vector Lyapunov stability results for discrete-time dynamical systems defined on N= (0,1,2,...,). We demonstrate the applicability of our results by considering a specific example