Model reduction via parameter matching using a Gramian technique

A model reduction technique based on parameter matching for single input single output (SISO) continuous systems is proposed. The reduced order models match various combinations (chosen by the designer) of four types of system invariant parameter of the full order system associated with low frequency response, high frequency response, low frequency power spectral density and high frequency power spectral density. In this way, selected parameters of both transient and steady state properties can be preserved in the model reduction process. Which parameters are chosen to be matched is contingent on those input/output properties of the original system that the designer considers most important to be retained in the reduced model. The number of parameters to be matched determines the order of the reduced model. The effectiveness of the matched parameters in retaining the input/output properties of the original system in the reduced models is fully investigated. The algorithm presented finds not one but the entire set (infinite) of reduced models that match a particular number of these parameters. Because the mix of parameters desired (i.e. the algorithm chosen) is at the discretion of the analyst, the new algorithm presented provides a handy assortment of techniques instead of a single `finished product´