Performance-based design of PI observers for fault diagnosis in LTI systems under Gaussian noises

This work addresses the fault diagnosis problem for LTI systems under the presence of Gaussian noises through model-based proportional-integral observers with predefined gains. We propose an integrated design of residual generators and evaluators which takes into account the trade-off between physically meaningful parameters such as the false alarm rate, the minimum isolable faults and the integral squared error of the residuals under step faults. Dynamical fault isolation is also taken into account. In order to solve this design problem, we present two different approaches: one based on the steady-state Kalman filter and another based on convex optimization techniques.