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Stability analysis and numerical simulations of a one dimensional open channel hydraulic system

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  • Chentouf, Boumediène
  • Smaoui, Nejib

Abstract

This paper is dedicated to the qualitative analysis as well as numerical simulations of a one dimensional open channel hydraulics system which is commonly used in hydraulic engineering to model the unsteady flow dynamics in a river. First, an output feedback control is proposed. Next, the closed-loop system is proved to possess a unique solution in a functional space. Furthermore, the spectrum and resolvent sets of the system operator are characterized. Then, stability results are stated and proved according to a smallness assumption on the feedback gain. The proof invokes Lyapunov direct method. Last but not least, we adopt the Chebychev collocation method, that uses backward Euler method and the Gauss-Lobatto points, to provide numerical simulations in order to ascertain the correctness of the theoretical outcomes.

Suggested Citation

  • Chentouf, Boumediène & Smaoui, Nejib, 2018. "Stability analysis and numerical simulations of a one dimensional open channel hydraulic system," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 498-511.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:498-511
    DOI: 10.1016/j.amc.2017.10.058
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    References listed on IDEAS

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    1. K. Ammari & B. Chentouf, 2010. "Further Results on the Robust Regulation of a One-Dimensional Dam-River System," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 597-606, December.
    2. Chentouf, Boumediène, 2015. "Stabilization of memory type for a rotating disk–beam system," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 227-236.
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    Cited by:

    1. Mean, Sovanna & Unami, Koichi & Okamoto, Hisashi & Fujihara, Masayuki, 2022. "A thorough description of one-dimensional steady open channel flows using the notion of viscosity solution," Applied Mathematics and Computation, Elsevier, vol. 415(C).

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