On output frequency-weighted controller reduction

An output frequency-weighted controller reduction method is considered. The rationale for reducing the controller order with such a setting is based on maintenance of stability and approximation of the original transfer function matrix considerations. U.M. Al-Saggaf and G.F. Franklin (1986) considered an input frequency-weighted controller reduction problem, but their method required that the matrix C of the weight (realized as a triplet (A, B, C) be square and nonsingular. Its dual is used to solve this problem by modifying the observability Gramian and then applying the basic balanced truncation technique to reduce the controller order. The advantage of using this approach is that only the matrix B is required to be of full column rank. An example is given to demonstrate this method