Perturbation analysis of eigenvalues of a class of self-adjoint operators

We consider a class of spatially invariant systems whose coefficients are perturbed by spatially periodic functions. We analyze changes in transient behavior under the effect of such perturbations. This is done by performing a spectral analysis of the state transition operator at every point in time. Computational complexity is significantly reduced by using a procedure that captures the influence of the perturbation on only the largest singular values of the state transition operator. Furthermore, we show that the problem of computing corrections of all orders to the maximum singular values collapses to that of finding the eigenvalues of a set of finite dimensional matrices. Finally, we demonstrate the predictive power of this method via an example.