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A Sampling Method and Approximation Results for Impulsive Systems

This paper studies an impulsive dynamical system that is in the form of a measure-driven differential inclusion. The employed solution concept depends upon a graph completion of the measure. The first main result shows that a subsequence of discrete-time trajectories graph-converges to a solution, and, under Lipschitz hypotheses, that every solution can be obtained in this manner. The second main result pursues a similar development with classical systems that approximate the given one.