Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 141867, 27 pages
Research Article

Fault Detection of Markov Jumping Linear Systems

School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, China

Received 10 December 2011; Accepted 1 February 2012

Academic Editor: Tadeusz Kaczorek

Copyright © 2012 Wei Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, the fault detection (FD) problems of discrete-time Markov jumping linear systems (MJLSs) are studied. We first focus on the stationary MJLS. The proposed FD system consists of two steps: residual generation and residual evaluation. A new reference model strategy is applied to construct a residual generator, such that it is robust against disturbances and sensitive to system faults. The generated residual signals are then evaluated according to their stochastic properties, and a threshold is computed for detecting the occurrences of faults. The upper bound of the corresponding false alarm rate (FAR) is also given. For the nonstationary MJLS, similar results are also obtained. All the solutions are presented in the form of linear matrix inequalities (LMIs). Finally, a numerical example is used to illustrate the results.