几何拉普拉斯变换：几何代数拉普拉斯变换的定义、存在性及性质
The geometric Laplace transform: Definition, existence and properties of the Geometric Algebra Laplace transform
- Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究针对动力系统建模与控制的需求，在几何代数框架下定义了拉普拉斯变换，其性质适用于符号特征≤5的几何代数，拓展了超复数代数相关变换的研究。
AI中文摘要：
近期已有研究开始探索几何代数（Geometric Algebra，GA）在动力系统建模、分析与控制，尤其是电路领域的应用。由于该领域的关键环节是将描述系统行为的动力系统常微分方程从实域变换到拉普拉斯域，因此需要定义GA框架下的拉普拉斯变换。本研究拓展了此前针对某些超复数代数的相关工作，引入了几何代数（GA）框架下的拉普拉斯变换定义，且该定义及其性质适用于符号特征不超过5的几何代数。
英文摘要：
Recent publications have started to explore the application of Geometric Algebra (GA) to the modeling, analysis and control of dynamical systems and, in particular, electrical circuits. Since a crucial element there is to transform the ordinary differential equations governing the dynamical system which models the systems' behavior from the real domain to the Laplace domain, a definition of the Laplace transform in GA is needed. In the present work, we extend previous works dealing with extension to some hiper-complex algebras by introducing a definition of the Laplace transform within the framework of Geometric Algebra (GA). In particular, our definition and its properties are applicable to geometric algebras with signature lower or equal than 5.
