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access icon free Optimal H i /H ∞ fault-detection filter design for uncertain linear time-invariant systems: an iterative linear matrix inequality approach

© The Institution of Engineering and Technology
Received 25/09/2012, Accepted 18/04/2013, Revised 12/04/2013, Published

An iterative linear matrix inequality (LMI) approach is proposed to design fault-detection filters (FDFs) of uncertain linear time-invariant (LTI) systems. The obtained FDF is the optimal solution for the H i /H ∞ (with H ∞/H ∞ and H −/H ∞ being two extreme cases) optimisation problem of FDF design and can achieve the best trade-off between robustness against unknown disturbances and sensitivity to system faults. The authors first derive the theoretical optimal H i /H ∞ FDFs for uncertain LTI systems based on the co-inner–outer factorisation technique. Then a new optimisation problem is formulated to obtain the optimal FDFs that can approach the theoretical optimal ones as much as possible. An iterative LMI approach is presented to find the solution in the state-space form. The effectiveness of the proposed approach is illustrated by a numerical example.

Inspec keywords: uncertain systems; fault diagnosis; linear systems; iterative methods; optimisation; control system synthesis; state-space methods; H∞ filters; matrix decomposition; linear matrix inequalities; optimal control

Other keywords: iterative linear matrix inequality approach; iterative LMI approach; LTI; optimisation problem; state-space form; FDF; uncertain linear time-invariant systems; co-inner–outer factorisation technique; optimal Hi-H∞ fault-detection filter design

Subjects: Linear algebra (numerical analysis); Interpolation and function approximation (numerical analysis); Signal processing theory; Optimal control; Optimisation techniques; Control system analysis and synthesis methods

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