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∞, ℋ2 / ℋ∞, and ℋ∞ / ℋ∞ problems, are the same and can be obtained by solving a standard algebraic Riccati equation. 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.