On solving periodic ℋ2-optimal fault detection and isolation problems

A lifting-free computational method is proposed to solve approximate fault detection and isolation problems for periodic systems using an ℋ₂-optimal model matching approach. The synthesis procedure relies on two key computational procedures: a numerically reliable algorithm to determine least order annihilators of periodic systems to reduce the periodic ℋ₂-optimal model matching problem to a simpler standard form and a recently developed algorithm to compute inner-outer factorizations of periodic systems which allows a further reduction to a ℋ₂ minimal distance problem. If the resulting fault detection filter is not stable and/or not causal, then a final stabilization step is performed using periodic coprime factorization techniques. The overall computational algorithm has strongly coupled computational steps, where all available structural information at the end of each computational step are fully exploited in the subsequent computations.