Partial stability of discontinuous dynamical systems

We develop results for partial stability of discontinuous dynamical systems (DDS) with respect to invariant sets defined on metric space, using stability preserving mappings. Our results are applicable to a much larger class of systems than existing results, including to DDS that cannot be determined by the usual (differential) equations or inequalities. Furthermore, in contrast to existing results which pertain primarily to the analysis of equilibria, the present results apply to invariant sets (including equilibria as special cases). We apply our results in the analysis of a special class of finite dimensional dynamical systems subject to impulse effects, and we show that in this particular case, our results are less conservative than existing ones.