Abstract
We first present several Lyapunov stability results (sufficient conditions as well as converse theorems) for a class of dynamical systems with discontinuous states. Examples of such systems include systems with impulse effects and discontinuous systems that arise in studies of hybrid dynamical systems. These results are then used in studying a specific class of switched dynamical systems and a specific class of dynamical systems with impulse effects. We show that the present results are more general and less conservative than existing results.
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