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Approximation of the Solution Set of Impulsive Systems

  • Tzanko Donchev
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4818)

Abstract

We investigate discrete approximation of the solution set of an impulsive differential inclusions with not fixed time of impulses (jumps) in finite dimensional Euclidean space. The right-hand side is assumed to be almost upper semi continuous and one sided Lipschitz. The fact that the impulsive times are not fixed posses problems and in the paper we study several variants of the Euler method in case of autonomous and not autonomous systems. The accuracy (in appropriate metric) of all considered variants is \(O(\sqrt{h})\). The results can be applied to impulsive optimal control problems.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Tzanko Donchev
    • 1
  1. 1.Department of MathematicsUniversity of Architecture and Civil EngineeringSofiaBulgaria

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