H∞ suboptimal model reduction for singular systems

H_∞ suboptimal model reduction for singular systems is investigated. First, the H_∞ norm is characterized for singular systems. Then an error system is established to measure the error magnitude between the original and reduced systems. The reduction of the singular system is based on decomposing the singular system into slow and fast subsystems. The reduced order models are computed by reducing the slow and fast systems separately. The slow system is reduced using standard balanced truncation or optimal Hankel norm approximation techniques. The fast system reduction is based on by making the error system between the original fast and reduced fast systems impulse free. The method is illustrated by numerical examples.