Combined Schur/L2 model reduction with fixed modes for discrete systems

A practical method of reducing a linear multiple-input multiple-output (MIMO) discrete-time system using a combination of aggregation, Schur and minimum principle methods is proposed. This method is based on computing the left and right eigenspace associated with the desired eigenvalues which are present in the original system. The method has the following useful features: the aggregation matrix can be obtained in a fairly straightforward manner: it is well-conditioned; the performance degradation is evaluated; and the DC gain mismatch of the original system and the reduced-order model is minimized. An example is given to demonstrate the effectiveness of the method. Application of the method to a fifth-order system indicates that a good reduced-order model can be achieved