A new approach to frequency weighted L2 optimal model reduction

This paper takes a new approach to the problem of frequency weighted L-2 optimal model reduction in the continuous case. Instead of trying to find an optimal reduced-order model, whose existence remains an unresolved issue, we consider the problem of seeking a reduced-order model with cost only differing from the optimal cost by a prescribed tolerance. It is shown that this problem can be reduced to a smooth constrained optimization problem which is guaranteed to admit a global minimum. A convergent gradient flow algorithm is proposed to solve the latter problem. Numerical results are presented to illustrate the effectiveness of this approach.