Discrete Approximation of Impulsive Differential Inclusions

Abstract

The article 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 [11] 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.

Keywords:

• Differential inclusions
• Discrete approximations
• Impulsive systems
• Reachable sets
• Variable times of impulses

AMS Subject Classification:

• Primary 34A37, 34A60
• Secondary 93B03, 49M25, 49K21

ACKNOWLEDGMENTS

This paper is dedicated to Frank Lempio on the occassion of his 65th birthday.

This work is supported by the Hausdorff Research Institute of Mathematics in Bonn within the framework of the Junior Trimester Program “Computational Mathematics” (February–April 2008).