Optimal robust fault detection for linear discrete time systems

This paper considers robust fault detection problems for linear discrete time systems. It is shown that the optimal robust detection filters for several well-recognized robust fault detection problems, such as H_-/H_infin, H₂/H_infin, and H_infin/H_infin problems, are the same and can be obtained by solving a standard algebraic Riccati equation. Moreover, the optimal filters for those problems do not depend on how the fault occurs, i.e., they are optimal for all possible faults under the optimization criteria. Optimal filters are also derived for many other optimization criteria and it is shown that some well-studied and seeming sensible optimization criteria for fault detection filter design could lead to (optimal but) useless fault detection filters.