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Mathematical Problems in Engineering
Volume 2016, Article ID 7249803, 14 pages
Research Article

Unitary Approximations in Fault Detection Filter Design

Department of Cybernetics and Artificial Intelligence, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, 042 00 Košice, Slovakia

Received 19 January 2016; Revised 17 March 2016; Accepted 28 March 2016

Academic Editor: Zehui Mao

Copyright © 2016 Dušan Krokavec 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.


The paper is concerned with the fault detection filter design requirements that relax the existing conditions reported in the previous literature by adapting the unitary system principle in approximation of fault detection filter transfer function matrix for continuous-time linear MIMO systems. Conditions for the existence of a unitary construction are presented under which the fault detection filter with a unitary transfer function can be designed to provide high residual signals sensitivity with respect to faults. Otherwise, reflecting the emplacement of singular values in unitary construction principle, an associated structure of linear matrix inequalities with built-in constraints is outlined to design the fault detection filter only with a Hurwitz transfer function. All proposed design conditions are verified by the numerical illustrative examples.