Closeness of Solutions for Singularly Perturbed Systems via Averaging

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Deghat, M; Ahmadizadeh, S; Nesic, D; Manzie, CDate
2018Source Title
Proceedings of the ... IEEE Conference on Decision & Control / IEEE Control Systems Society. IEEE Conference on Decision & ControlPublisher
IEEEUniversity of Melbourne Author/s
Ahmadizadeh, Saeed; Nesic, Dragan; Manzie, Christopher; Deghat, MohammadAffiliation
Electrical and Electronic EngineeringMetadata
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Conference PaperCitations
Deghat, M., Ahmadizadeh, S., Nesic, D. & Manzie, C. (2018). Closeness of Solutions for Singularly Perturbed Systems via Averaging. Proceedings of the 2018 IEEE Conference on Decision and Control (CDC), 2018-December, pp.3110-3115. IEEE. https://doi.org/10.1109/CDC.2018.8619270.Access Status
Open AccessARC Grant code
ARC/DP170104102Abstract
This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary layer solutions converge to a bounded set, results on the closeness of solutions of the singularly perturbed system to the solutions of the reduced average and boundary layer systems over a finite time interval are presented. The closeness of solutions error is shown to be of order O (√{ε}), where ε is the perturbation parameter.
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