Closeness of Solutions for Singularly Perturbed Systems via Averaging

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    Author
    Deghat, M; Ahmadizadeh, S; Nesic, D; Manzie, C
    Date
    2018
    Source Title
    Proceedings of the ... IEEE Conference on Decision & Control / IEEE Control Systems Society. IEEE Conference on Decision & Control
    Publisher
    IEEE
    University of Melbourne Author/s
    Ahmadizadeh, Saeed; Nesic, Dragan; Manzie, Christopher; Deghat, Mohammad
    Affiliation
    Electrical and Electronic Engineering
    Metadata
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    Document Type
    Conference Paper
    Citations
    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 Access
    URI
    http://hdl.handle.net/11343/251417
    DOI
    10.1109/CDC.2018.8619270
    ARC Grant code
    ARC/DP170104102
    Abstract
    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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