IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i8p1330-d396911.html
   My bibliography  Save this article

Revisiting the 1D and 2D Laplace Transforms

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/8/1330/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/8/1330/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vogel, Everton & Beber, Caetano Luiz, 2021. "Sustainable Intensification Strategies for GHG Mitigation Among Heterogeneous Dairy Farms in Paraná, Brazil," 2021 Conference, August 17-31, 2021, Virtual 315219, International Association of Agricultural Economists.
    2. Aldona Standar & Agnieszka Kozera, 2020. "Identifying the Financial Risk Factors of Excessive Indebtedness of Rural Communes in Poland," Sustainability, MDPI, vol. 12(3), pages 1-25, January.
    3. Jorge Muñoz & Francesco Piqué & Concepción A. Monje & Egidio Falotico, 2021. "Robust Fractional-Order Control Using a Decoupled Pitch and Roll Actuation Strategy for the I-Support Soft Robot," Mathematics, MDPI, vol. 9(7), pages 1-16, March.
    4. Isadora Luiza Climaco Cunha & Fábio Rosa & Luiz Kulay, 2021. "Green Coalescent Synthesis Based on the Design for Environment (DfE) Principles: Brazilian Experience," Sustainability, MDPI, vol. 13(22), pages 1-22, November.
    5. Gerson Javier Pérez-Valbuena & Jaime Bonet-Morón, 2018. "Municipal Fiscal Health in Colombian Main Cities," Documentos de Trabajo Sobre Economía Regional y Urbana 17016, Banco de la República, Economía Regional.
    6. Simon J Williams & Sharon Boden, 2004. "‘Consumed with Sleep? Dormant Bodies in Consumer Culture’," Sociological Research Online, , vol. 9(2), pages 98-109, May.
    7. Michalopoulos, T. & Oude Lansink, Alfons G.J.M. & Heuvelink, E. & Hogeveen, Henk, 2008. "Multi-criteria assessment of ethical aspects in fresh tomato systems: Plant genomics technology innovation and food policy uses," 2008 International Congress, August 26-29, 2008, Ghent, Belgium 44147, European Association of Agricultural Economists.
    8. Manuel Henriques & Duarte Valério & Paulo Gordo & Rui Melicio, 2021. "Fractional-Order Colour Image Processing," Mathematics, MDPI, vol. 9(5), pages 1-15, February.
    9. Inés Tejado & Emiliano Pérez & Duarte Valério, 2020. "Fractional Derivatives for Economic Growth Modelling of the Group of Twenty: Application to Prediction," Mathematics, MDPI, vol. 8(1), pages 1-21, January.
    10. Manuel Sousa & Maria Fatima Almeida & Rodrigo Calili, 2021. "Multiple Criteria Decision Making for the Achievement of the UN Sustainable Development Goals: A Systematic Literature Review and a Research Agenda," Sustainability, MDPI, vol. 13(8), pages 1-37, April.
    11. Raquel Miranda & Susana Vinga & Duarte Valério, 2020. "Studying Bone Remodelling and Tumour Growth for Therapy Predictive Control," Mathematics, MDPI, vol. 8(5), pages 1-22, May.
    12. Daniel Cao Labora & José António Tenreiro Machado, 2020. "Existence of Bounded Solutions to a Modified Version of the Bagley–Torvik Equation," Mathematics, MDPI, vol. 8(2), pages 1-11, February.
    13. Inés Tejado & Blas M. Vinagre & José Emilio Traver & Javier Prieto-Arranz & Cristina Nuevo-Gallardo, 2019. "Back to Basics: Meaning of the Parameters of Fractional Order PID Controllers," Mathematics, MDPI, vol. 7(6), pages 1-16, June.
    14. Santiago Garrido & Concepción A. Monje & Fernando Martín & Luis Moreno, 2020. "Design of Fractional Order Controllers Using the PM Diagram," Mathematics, MDPI, vol. 8(11), pages 1-18, November.
    15. Cristian Pérez-Caselles & Margarita Brugarolas & Laura Martínez-Carrasco, 2020. "Traditional Varieties for Local Markets: A Sustainable Proposal for Agricultural SMEs," Sustainability, MDPI, vol. 12(11), pages 1-19, June.
    16. Dongxiao Niu & Hao Zhen & Min Yu & Keke Wang & Lijie Sun & Xiaomin Xu, 2020. "Prioritization of Renewable Energy Alternatives for China by Using a Hybrid FMCDM Methodology with Uncertain Information," Sustainability, MDPI, vol. 12(11), pages 1-26, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1330-:d:396911. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.