Super-optimal model reduction in sense of Hankel-norm

The best approximation in the optimal solution set of the Hankel-norm model reduction problem is studied in this paper since the optimal solutions are not unique for linear multi-input-multi-output systems (matrix-value transfer functions). This kind of model reduction problems will be defined properly and intuitively. The sub-layers of the optimal model errors will be characterized by the appropriate Schmidt pairs. The optimal solution set will also be parametrized in the suitable domain in order to keep the reduced model with the constant order after the optimatizations. The results from this proposed approach show that they are better than those from the other optimal approximate models in sense of the Hankel operator singular values.