Direct Shaping of Minimum and Maximum Singular Values: An $\mathcal{H}_{-}/\mathcal{H}_{\infty}$ Synthesis Approach for Fault Detection Filters

The performance of fault detection filters relies on a high sensitivity to faults and a low sensitivity to disturbances. The aim of this paper is to develop an approach to directly shape these sensitivities, expressed in terms of minimum and maximum singular values. The developed method offers an alternative solution to the $\mathcal{H}_{-}/\mathcal{H}_{\infty}$ synthesis problem, building upon traditional multiobjective synthesis results. The result is an optimal filter synthesized via iterative convex optimization and the approach is particularly useful for fault diagnosis as illustrated by a numerical example.