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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 528932, 13 pages
Research Article

LMI-Based Sliding Mode Observers for Incipient Faults Detection in Nonlinear System

1College of Electrical and Information Engineering, Hunan University of Technology, Hunan, Zhuzhou 412008, China
2College of Mechatronic Engineering and Automation, National University of Defense Technology, Hunan, Changsha 410073, China
3Wind Power Department, CSR Zhuzhou Institute Co., Ltd., Hunan, Zhuzhou 412001, China

Received 26 August 2012; Accepted 11 November 2012

Academic Editor: Xinzhi Liu

Copyright © 2012 Chang-fan Zhang 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 presents a diagnosis scheme based on a linear matrix inequality (LMI) algorithm for incipient faults in a nonlinear system class with unknown input disturbances. First, the nonlinear system is transformed into two subsystems, one of which is unrelated to the disturbances. Second, for the subsystem that is free from disturbances, a Luenberger observer is constructed; a sliding mode observer is then constructed for the subsystem which is subjected to disturbances, so that the effect of the unknown input disturbances is eliminated. Together, the entire system achieves both robustness to disturbances and sensitivity to incipient faults. Finally, the effectiveness and feasibility of the proposed method are verified through a numerical example using a single-link robotic arm.