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Revisiting the 1D and 2D Laplace Transforms

Author

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  • Manuel Duarte Ortigueira

    (CTS-UNINOVA and DEE of NOVA School of Science and Technology, 2829-516 Caparica, Portugal
    Current address: Campus of NOVA School of Science and Technology, Quinta da Torre, 2829-516 Caparica, Portugal.
    These authors contributed equally to this work.)

  • José Tenreiro Machado

    (Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, 431 4249-015 Porto, Portugal
    Current address: Campus of NOVA School of Science and Technology, Quinta da Torre, 2829-516 Caparica, Portugal.
    These authors contributed equally to this work.)

Abstract

The paper reviews the unilateral and bilateral, one- and two-dimensional Laplace transforms. The unilateral and bilateral Laplace transforms are compared in the one-dimensional case, leading to the formulation of the initial-condition theorem. This problem is solved with all generality in the one- and two-dimensional cases with the bilateral Laplace transform. The case of fractional-order systems is also included. General two-dimensional linear systems are introduced and the corresponding transfer function is defined.

Suggested Citation

  • Manuel Duarte Ortigueira & José Tenreiro Machado, 2020. "Revisiting the 1D and 2D Laplace Transforms," Mathematics, MDPI, vol. 8(8), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1330-:d:396911
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    References listed on IDEAS

    as
    1. Shervin Erfani & Nima Bayan, 2013. "Characterisation of nonlinear and linear time-varying systems by Laplace transformation," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(8), pages 1450-1467.
    2. João Clímaco & João Paulo Costa & Gregory Kersten, 2015. "Introduction," Group Decision and Negotiation, Springer, vol. 24(4), pages 563-566, July.
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    Cited by:

    1. Manuel D. Ortigueira, 2022. "A New Series Representation and the Laplace Transform for the Lognormal Distribution," Mathematics, MDPI, vol. 10(19), pages 1-13, September.
    2. Manuel D. Ortigueira, 2022. "A New Look at the Initial Condition Problem," Mathematics, MDPI, vol. 10(10), pages 1-17, May.
    3. António M. Lopes & J. A. Tenreiro Machado, 2022. "Nonlinear Dynamics," Mathematics, MDPI, vol. 10(15), pages 1-3, July.
    4. Müfit Şan & Manuel D. Ortigueira, 2022. "Unilateral Laplace Transforms on Time Scales," Mathematics, MDPI, vol. 10(23), pages 1-21, December.
    5. Duarte Valério & Manuel D. Ortigueira & António M. Lopes, 2022. "How Many Fractional Derivatives Are There?," Mathematics, MDPI, vol. 10(5), pages 1-18, February.

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