Optimal solutions to multi-objective robust fault detection problems

This paper will give complete, analytic, and optimal solutions to several robust fault detection problems that have been considered in the research community in the last twenty years. It is shown that several well-recognized robust fault detection problems, such as H_-/H_infin, H₂/H_infin, and H_infin/H_infin problems, have a very simple optimal solution in an observer form by solving a standard algebraic Riccati equation. Moreover, the optimal filter does not depend on how the fault occurs, i.e., it is optimal for all possible faults under the optimization criteria. It is also shown that some well-studied and seeming sensible optimization criteria for fault detection filter design could lead to (optimal but) useless fault detection filter designs.