Optimal Hi/H∞ Fault Detection Filter Design: An Iterative LMI Approach

In this paper, a linear matrix inequality (LMI) based approach is proposed for the design of fault detection filter (FDF) which can achieve the best trade-off between robustness against unknown disturbances and sensitivity to system faults. We first analyze the the performance index H-i/H-infinity measuring the trade-off in all directions of the residual space, and then propose a new design index computed with the maximum and minimum nonzero singular values of the transfer function from disturbances to residual. The necessary and sufficient condition for checking whether an FDF is optimal or not, is given in terms of matrix inequalities (MI). An iterative linear matrix inequality (ILMI) algorithm is finally developed to design the optimal FDF based on the proposed design index. With the obtained FDF, the H-infinity/H-infinity and H-/H-infinity indexes are optimized as two extreme cases. A numerical example is given to illustrate the effectiveness of the proposed approach.