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A generalization of the Tikhonov theorem for singularly perturbed differential inclusions

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Abstract

We study the continuity properties of the bundle of solutions to a differential inclusion subject to a singular perturbation, i.e., with respect to a scalar parameter ɛ multiplying a part of the derivatives. We give conditions under which every solution of the singularly perturbed inclusion is close, in a certain sense and for a sufficiently small ɛ, to a solution of the degenerate inclusion obtained for ɛ=0. These conditions include both stability and structural requirements (the later having no counterpart in the case of a differential equation). The main result obtained generalizes the well-known Tikhonov theorem for singularly perturbed differential equations.

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Authors and Affiliations

  1. Institute of Operations Research and Statistics, University of Vienna, Universitätsstrasse 5, A-1010, Vienna, Austria

    V. Veliov

  2. Institute of Mathematics, Bulgarian Academy of Sciences, P.O.Box 373, 1113, Sofia, Bulgaria

    V. Veliov

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  1. V. Veliov
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Veliov, V. A generalization of the Tikhonov theorem for singularly perturbed differential inclusions. Journal of Dynamical and Control Systems 3, 291–319 (1997). https://doi.org/10.1007/BF02463254

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  • DOI: https://doi.org/10.1007/BF02463254

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