High-order eigenproblem sensitivity methods: theory and application to the design of linear dynamical systems†

In a previous paper (Crossley and Porter 1969) simple and explicit derivations were given for the first-order eigenvalue and eigenvector sensitivity coefficients for the Fundamental eigenproblem associated with the behaviour of linear dynamical systems governed by equations of the form [xdot] = Ax. In the present paper, similar techniques are used to derive the corresponding second-order eigenvalue and eigenvector sensitivity coefficients. The second-order theory is then applied to two examples in order to compare the results obtainable from this theory with the corresponding results obtainable from the first-order theory and from exact calculations.