Eigenvalue tracking due to parameter variation

This note describes an efficient eigenvalue tracking algorithm, which is applicable in many engineering systems where the effect of parameter variation on system stability is to be determined. Starting with the original system eigenvalues, the algorithm uses determinants to compute first-order eigenvalue sensitivities which are used in an iterative method that converges rapidly to the new eigenvalues corresponding to the parameter change. The algorithm tracks all the system eigenvalues starting from a given base case. It is shown to be less costly than repeated eigenvalue evaluation and is illustrated by means of a simple power system example.