A time-domain solution approach to model reduction

Theoretical limitations for model reduction systems described by ordinary differential equations are investigated through use of the system solution rather than the system state equations. The general case is discussed first and the specialized to linear time-varying systems and finally to linear time-invariant systems. The distance between the original and reduced systems is measured by an error norm corresponding to energy. The reduction method is based on partition of the state space into two orthogonal subspaces. It is an effective procedure which works for both stable and unstable systems but requires knowledge of the system solution in order to be applied. In general the reduced-order model cannot be separated from the initial conditions, but this is possible for linear systems. If there is a driving function acting on the system, it will affect the reduced-order model in an essential way, and its order then cannot in general be reduced