Conclusions A computationally efficient algorithm has been presented for obtaining the complex Fourier transform of a class of vector functions that frequently occur in modern control theory. The basic algorithm requires 1) the evaluation of a single matrix exponential for the dynamics of the time-varying control; 2) the solution for either the right and left eigenvectors or a real Schur decomposition of the constant control dynamics matrix; 3) the sequential solution for the reducing subspace transformation vector p; and 4) the evaluation of a single scalar complex exponential.