A Geometric Approach to Fault Detection and Isolation of Continuous-Time Markovian Jump Linear Systems
A Geometric Approach to Fault Detection and Isolation of Continuous-Time Markovian Jump Linear Systems
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DOI：
10.1109/tac.2010.2042007
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发表时间：
2010-02
影响因子：
6.8
通讯作者：
N. Meskin;K. Khorasani
中科院分区：
文献类型：
--
作者：
N. Meskin;K. Khorasani
本文研究了马尔可夫跳变线性系统和时滞跳变线性系统的故障检测与隔离策略。首先，提出了与MJLS的不可观测子空间有关的几何性质。有限不可观测子空间的概念，然后介绍了MJLSD的。对MJLS和MJLSD引入了不可观测子空间的概念，并给出了构造不可观测子空间的算法。利用我们引入的不可观测子空间，给出了MJLS的残差生成基本问题（FPRG）可解的充要条件。此外，还导出了MJLSD的FPRG可解的充分条件。最后，针对具有未知转移矩阵的MJLS系统，给出了设计基于H∞的FDI算法的充分条件。
This paper is concerned with development of novel fault detection and isolation (FDI) strategies for the Markovian jump linear systems (MJLS's) and the MJLS's with time-delays (MJLSD's). First a geometric property that is related to the unobservable subspace of MJLS's is presented. The notion of a finite unobservable subspace is then introduced for the MJLSD's. The concept of unobservability subspace is introduced for both the MJLS's and the MJLSD's and an algorithm for its construction is described. The necessary and sufficient conditions for solvability of the fundamental problem of residual generation (FPRG) for the MJLS's are developed by utilizing our introduced unobservability subspace. Furthermore, sufficient solvability conditions of the FPRG for the MJLSD's are also derived. Finally, sufficient conditions for designing an H∞-based FDI algorithm for the MJLS's with an unknown transition matrix that are also subject to input and output disturbances are developed.