Bilinear transformation and generalized singular perturbation model reduction

A new general bilinear relationship is found between continuous and discrete generalized singular perturbation reduced-order models. This result is applied to the problem of deriving discrete analogs 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.