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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 231749, 11 pages
http://dx.doi.org/10.1155/2015/231749
Research Article

Observer-Based Robust Fault Detection Filter Design and Optimization for Networked Control Systems

1School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
2The Flight Automatic Control Research Institute of AVIC, Xi’an, Shaanxi 710065, China
3School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

Received 4 April 2014; Accepted 17 August 2014

Academic Editor: Minrui Fei

Copyright © 2015 Weilai Jiang 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.

Abstract

The problem of robust fault detection filter (FDF) design and optimization is investigated for a class of networked control systems (NCSs) with random delays. The NCSs are modeled as Markovian jump systems (MJSs) by assuming that the random delays obey a Markov chain. Based on the model, an observer-based residual generator is constructed and the corresponding fault detection problem is formulated as an filtering problem by which the error between the residual signal and the fault is made as small as possible. A sufficient condition for the existence of the desired FDF is derived in terms of linear matrix inequalities (LMIs). Furthermore, to improve the performance of the robust fault detection systems, a time domain optimization approach is proposed. The solution of the optimization problem is given in the form of Moore-Penrose inverse of matrix. A numerical example is provided to illustrate the effectiveness and potential of the proposed approach.