Revisiting the 1D and 2D Laplace Transforms

被引：26

作者：

Ortigueira, Manuel Duarte ^{[1
,2
,4
]}

Machado, Jose Tenreiro ^{[3
,4
]}

机构：

[1] CTS UNINOVA, P-2829516 Caparica, Portugal

[2] NOVA Sch Sci & Technol, DEE, P-2829516 Caparica, Portugal

[3] Polytech Porto, Dept Elect Engn, Inst Engn, P-431424901 Porto, Portugal

[4] Campus NOVA Sch Sci & Technol, P-2829516 Caparica, Portugal

来源：

MATHEMATICS | 2020年 / 8卷 / 08期

关键词：

laplace transform; two-dimensional laplace transform; initial-conditions; two-dimensional linear systems; ELECTRIC-CIRCUIT THEORY;

D O I：

10.3390/math8081330

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：24

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