Optimal reduction of linear systems

The use of direct search (LJ) optimization procedure in multi-pass manner in the fre-quency domain is shown to be a viable approach for obtaining the optimal reduced model of a linear single-input single-output (SISO) system, for which the optimal solution has eluded previous investigators. The resulting second-order reduced model provides very close time-domain response of the original model to both impulse and step inputs. Establishment of the third-order reduced model is computationally more demanding. Similar behaviour is observed with an eigth-order transfer function, where the second-order reduced model is very easily obtained, but higher order reduced models require a considerably larger number of random points to be used in each iteration.