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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 2740645, 17 pages
Research Article

Minimal-Order Functional Observer-Based Residual Generators for Fault Detection and Isolation of Dynamical Systems

School of Engineering, Deakin University, Geelong, VIC 3217, Australia

Received 10 January 2016; Revised 22 March 2016; Accepted 5 April 2016

Academic Editor: Zehui Mao

Copyright © 2016 H. M. Tran and H. Trinh. 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 examines the design of minimal-order residual generators for the purpose of detecting and isolating actuator and/or component faults in dynamical systems. We first derive existence conditions and design residual generators using only first-order observers to detect and identify the faults. When the first-order functional observers do not exist, then based on a parametric approach to the solution of a generalized Sylvester matrix equation, we develop systematic procedures for designing residual generators utilizing minimal-order functional observers. Our design approach gives lower-order residual generators than existing results in the literature. The advantages for having such lower-order residual generators are obvious from the economical and practical points of view as cost saving and simplicity in implementation can be achieved, particularly when dealing with high-order complex systems. Numerical examples are given to illustrate the proposed fault detection and isolation schemes. In all of the numerical examples, we design minimum-order residual generators to effectively detect and isolate actuator and/or component faults in the system.