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Journal of Applied Mathematics
Volume 2013, Article ID 829715, 12 pages
Research Article

Robust Fault Detection of Linear Uncertain Time-Delay Systems Using Unknown Input Observers

1Electrical Engineering Department, Iran University of Science and Technology, Narmak, Tehran 16846, Iran
2Department of Electrical and Electronic Engineering, Shiraz University of Technology, Shiraz 71557-13876, Iran
3Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway

Received 18 July 2013; Accepted 13 September 2013

Academic Editor: Baocang Ding

Copyright © 2013 Saeed Ahmadizadeh 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.


This paper deals with the problem of fault detection for linear uncertain time-delay systems. The proposed method for Luenberger observers is developed for unknown input observers (UIOs), and a novel procedure for the design of residual based on UIOs is presented. The design procedure is carried out based on the model matching approach which minimizes the difference between generated residuals by the optimal observer and those by the designed observer in the presence of uncertainties. The optimal observer is designed for the ideal system and works so that the fault effect is maximized while the exogenous disturbances and noise effects are minimized. This observer can give disturbance decoupling in the presence of noise and uncertainties for linear uncertain time-delay systems. The developed method is applied to a numerical example, and the simulation results show that the proposed approach is able to detect faults reliably in the presence of modeling errors, disturbances, and noise.