Revisiting the 1D and 2D laplace transforms

Manuel Duarte Ortigueira, José Tenreiro Machado

Research output: Contribution to journalReview articlepeer-review

27 Citations (Scopus)
81 Downloads (Pure)


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.

Original languageEnglish
Article number1330
Issue number8
Publication statusPublished - 10 Aug 2020


  • Initial-conditions
  • Laplace transform
  • Two-dimensional laplace transform
  • Two-dimensional linear systems


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