On eigenvalue ranking indices for continuous linear time invariant systems

The assessment of the importance of each single eigenvalue by deriving accurate ranking indices is discussed. The essential or critical modes are defined as the ones that contribute the most to a prespecified quadratic performance index, e.g. output energy function. Specifically, three ranking methods for continuous linear time-invariant systems are proposed. The first method is to use the results of A. Feliachi (IEEE Trans. Power Syst., vol.5, no.3, p.783-7, 1990) and derive a new separation method of the overall contribution index in ranking indices. The second approach, called the weighting factor ranking index, is based on the relative importance of joint eigenvalue contributions to the energy function. Finally, a remainder ranking index based on the least contribution to the energy function when the eigenvalue of concern is ignored is derived. A comparison of all these methods is given.<>