Bilinear transformation and generalised singular perturbation model reduction

A new general bilinear relationship is found between continuous and discrete generalised singular perturbation (GSP) reduced order models. This result is applied to the problem of deriving discrete analogues of continuous singular perturbation and direct truncation model reduction, and leads to a new definition of discrete “Nyquist” model reduction. Also, “unit circle” bilinear transformations are used to relate several known facts about continuous and discrete balanced model reduction and incorporate them into a symmetrical, unified framework