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

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.