论文标题
线性结构化系统的故障检测和隔离
Fault detection and isolation for linear structured systems
论文作者
论文摘要
本文介绍了线性结构化系统的故障检测和隔离问题（FDI）问题，其中系统矩阵由零/非零/任意模式矩阵给出。在本文中，我们遵循一种几何方法来验证此类系统的外国直接投资问题的解决性。为此，我们首先开发出一种必要且充分的条件，在该条件下，可以解决特定的线性时间存在系统的FDI问题。接下来，我们为线性结构化系统的外国直接投资问题的可溶性建立了必要条件。此外，我们开发了一个足够的代数条件，可以根据相关模式矩阵的等级测试来解决外国直接投资问题的可溶性。为了说明这种条件不是必需的，我们提供了一个反例，在该例子中，在不满足条件的情况下，FDI问题是可以解决的。最后，我们为给定模式矩阵的完整等级属性开发了图形理论条件，这导致了FDI问题可溶解性的图理论条件。
This paper deals with the fault detection and isolation (FDI) problem for linear structured systems in which the system matrices are given by zero/nonzero/arbitrary pattern matrices. In this paper, we follow a geometric approach to verify solvability of the FDI problem for such systems. To do so, we first develop a necessary and sufficient condition under which the FDI problem for a given particular linear time-invariant system is solvable. Next, we establish a necessary condition for solvability of the FDI problem for linear structured systems. In addition, we develop a sufficient algebraic condition for solvability of the FDI problem in terms of a rank test on an associated pattern matrix. To illustrate that this condition is not necessary, we provide a counterexample in which the FDI problem is solvable while the condition is not satisfied. Finally, we develop a graph-theoretic condition for the full rank property of a given pattern matrix, which leads to a graph-theoretic condition for solvability of the FDI problem.
