Computing bounds for a simple fault detection scheme

A deterministic approach is presented for computing thresholds in a simple fault detection system. The thresholds measure the magnitude of the minimum detectable fault and the maximum nondetectable fault. Two different approaches are presented here. The first is the use of the 2-norm which results in a linear matrix inequality (LMI) problem and the second is the use of the l_∞-norm which results in an integer linear programming problem. A filter design is proposed in both cases that enhances the ability to distinguish between the fault and the disturbance.