论文标题
图案矩阵的属性，并应用于结构化系统
Properties of pattern matrices with applications to structured systems
论文作者
论文摘要
数学模型的确切参数值通常不确定甚至未知。但是，我们可能可以访问有关参数的粗略信息，例如，其中一些是非零的。可以通过所谓的模式矩阵捕获此类信息，其符号条目用于表示有关相应参数的可用信息。在本文中，我们专注于具有三种符号条目的模式矩阵：代表零，非零和任意参数的矩阵。我们正式定义并研究了这种模式矩阵的添加和乘法。然后将结果用于研究三种强结构特性的研究，即线性描述器系统的可控性以及线性系统的输入状态可观察性和输出可控性。
The exact parameter values of mathematical models are often uncertain or even unknown. Nevertheless, we may have access to crude information about the parameters, e.g., that some of them are nonzero. Such information can be captured by so-called pattern matrices, whose symbolic entries are used to represent the available information about the corresponding parameters. In this paper, we focus on pattern matrices with three types of symbolic entries: those that represent zero, nonzero, and arbitrary parameters. We formally define and study addition and multiplication of such pattern matrices. The results are then used in the study of three strong structural properties, namely, controllability of linear descriptor systems, and input-state observability and output controllability of linear systems.
