On Eigenvalue Ranking Indices

Large-scale system In general have a large number of eigenvalues. For son applications such as output feedback control design, reduced order modeling and simulation, only a few of these eigevalues are crucial. An robust eigenvalue ranking procedure is proposed In this paper. Some previous work on eigenvalue estimation when the system is subject to perturbation has been proposed by several researchers. However, there is not such work done on eigenvalue ranking when a perturbation is present. The eigenvalue ranking approach presented in this work is based on the contribution of each eigenvalue to a quadratic measure. The ranting corresponding to the nominal model will be called the ´nominal ranking.´ An algorithm Is proposed to estimate the changes of the nminal ranking when the system is under perturbations.