Robust Sampled-Data Fault Detection Filtering Through Differential Linear Matrix Inequalities

This letter aims to design optimal and robust
$H_{\infty }$
fault detection filters for linear sampled-data systems. In particular, convex design conditions are derived in terms of differential linear matrix inequalities (DLMIs) for optimal, time-varying,
$H_{\infty }$
fault detection filters. The results are specialized to recast the optimal filter structure into a time-invariant, internal model-based, observer formulation. Furthermore, the robust case, in which the plant is uncertain is also tackled. We present an illustrative example to show the effectiveness of our results compared with the ones available in the literature.