Discrete-time model reduction with optimal zero locations by norm minimization

A hybrid approach is used to design reduced order discrete time models. First, the reduced order model denominator is fixed either by choosing its roots to be those nearest to the unit circle (i.e., the dominant poles of the original model), or by any other method. Then the numerator zeros are chosen optimally so that certain norms on the approximation error is minimized, while at the same time-satisfying some of the linear constraints. Several norms are used (l₂, l_∞, l_l), and it is shown how to compute the optimal solution in each case. An example is worked out to illustrate the efficiency of the proposed methods