Eigenvalue sensitivity in multivariable systems

Results obtained in the evaluation of the sensitivity of eigenvalues of a closed-loop system to the perturbations in the gain elements are presented. A basis for the gain vector space is developed using large-scale perturbations of the eigenvalues such that movement of the gain vector along a direction in this space affects the position of only one real eigenvalue or of a complex conjugate pair of eigenvalues. It is shown that this basis can be used to directly compute the incremental sensitivities of the eigenvalues to the individual gain vector elements. Numerical examples are included to illustrate these theoretical concepts.<>