二阶奇异差分方程系统的指数约化
Index Reduction for Second Order Singular Systems of Difference Equations
摘要：
本文研究了二阶线性离散广义系统（或带控制的奇异差分方程）的稳定性。在Kunkel和Mehrmann提出的矩阵值函数束的代数方法的基础上，首先给出了一个基于约化过程的理论框架来分析边值问题的初值问题的可解性，然后对广义系统进行了分析。我们还描述了方法来分析这些系统的可解性分析相关的结构特性。也就是说，两个数值算法减少到所谓的strangenessfree形式。两个相关的索引概念也介绍和讨论。本文的工作推广和补充了高阶连续广义系统和一阶离散广义系统的一些最新结果。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
