A sampling method and approximation results for impulsive systems

Abstract

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. © 2007 Society for Industrial and Applied Mathematics.