Hankel-norm model reduction with fixed modes

A constrained Hankel-norm approximation problem is considered. The reduced-order model is required to retain as a subset of its poles some prescribed eigenvalues from the original system. The constraint approximation problem is solved with an optimal Hankel-norm criterion, and an L^∞ error bound for the approximation error is provided. The proposed method for model reduction can be described as a partial eigenvalue preservation method. The reduced-order model is allowed to have a set of free poles in addition to eigenvalues which are preserved from the original system because of physical considerations. Although the method can be used in conjunction with the dominant mode concept, it is equally feasible to retain some eigenvalues of particular interest (but otherwise nondominant) and let the free poles take care of the dominant characteristics of the system