Discrete Approximation of Impulsive Differential Inclusions

R. Baier, T. D. Donchev: Discrete Approximation of Impulsive Differential Inclusions
22 pages, University of Bonn, September 2009

Smart-Link: http://www.hausdorff-research-institute.uni-bonn.de/files/preprints/Baier_Donchev_Discr_Approx_Impulsive_DI_HIM.pdf
Keywords: impulsive differential inclusions; numerical approximation of the solution set and the reachable set; Euler's method; convergence order; evaluation of the jump conditions
Mathematics Subject Classification Code: 34A37 (93B03 34A60 49M25)
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Abstract:

The paper deals with the approximation of the solution set and the reachable sets of an impulsive differential inclusion with variable times of impulses. It is strongly connected to T. Donchev, ``Approximation of the Solution Set of Impulsive Systems", Lecture Notes in Comput. Sci. 4818 (2008) and is its continuation. We achieve order of convergence 1 for the Euler approximation under Lipschitz assumptions on the set-valued right-hand side and on the functions describing the jump surfaces and jumps themselves. Another criterion prevents the beating phenomena and generalizes available conditions. Several test examples illustrate the conditions and the practical evaluation of the jump conditions.

Contents:

1. Preliminaries
2. Approximation of the solution set
3. Approximation of the reachable set

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