Model Reduction in the Frequency Domain

A linear transfer function of a process model in the Laplace domain can be given by  

Suppose it is required to find a reduced transfer function model, given by  

The reduced model should represent the original process as closely as possible. In order to compare the performance of the reduced model to the more complex model, one could define a quadratic performance criterion, such as  

Because of the latter limitation, many authors suggest to redefine Eqn (26.3) for the frequency domain. The deviations between the original system and the reduced system are then minimized over a particular frequency range. 

Process Dynamics and Control Modeling fior Control and Prediction. Brian Roffel and Ben Betlem. 2006 John Wiley Sons Ltd. 

---