Optimal Robust Fault Detection for Linear Discrete Time Systems

Abstract

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 ∞ , ℋ 2 / ℋ ∞ , and ℋ ∞ / ℋ ∞ problems, are the same and can be obtained by solving a standard algebraic Riccati equatio n. 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.