论文标题
二阶差异方程式二阶单数系统的索引减少
Index Reduction for Second Order Singular Systems of Difference Equations
论文作者
论文摘要
本文致力于分析线性二阶离散时间描述符系统（或具有控制的奇异差方程（侧））。遵循Kunkel和Mehrmann针对基质有价值函数铅笔提出的代数方法，首先，我们基于降低程序来提出一个理论框架，以分析侧面的初始价值问题的溶解度，随后是描述符系统的分析。我们还描述了分析与这些系统的溶解性分析相关的结构特性的方法。也就是说，提出了两种用于还原为所谓的陌生形式的数值算法。还引入和讨论了两个相关的索引概念。这项工作扩展并补充了高阶连续时间描述系统和一阶离散时间描述符系统的一些最新结果。
This paper is devoted to the analysis of linear second order discrete-time descriptor systems (or singular difference equations (SiDEs) with control). Following the algebraic approach proposed by Kunkel and Mehrmann for pencils of matrix valued functions, first we present a theoretical framework based on a procedure of reduction to analyze solvability of initial value problems for SiDEs, which is followed by the analysis of descriptor systems. We also describe methods to analyze structural properties related to the solvability analysis of these systems. Namely, two numerical algorithms for reduction to the so-called strangenessfree forms are presented. Two associated index notions are also introduced and discussed. This work extends and complements some recent results for high order continuous-time descriptor systems and first order discrete-time descriptor systems.
