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

A hybrid approach is used to design reduced-order discrete time models. 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 are minimised, while at the same time satisfying some linear constraints. Several norms are used (l₂, l_∞ and l₁), and the optimal solution is computed for each case. Two examples illustrate the efficiency of the proposed methods