The state-space approach to first-order perturbations in electrical networks

First-order perturbation theory is used to find the shifts in the eigenvalues of the state matrix due to changes in the values of the reactive elements and due to the introduction of losses in electrical networks. A set of simultaneous equations are found to realize the invariance of the eigenvalues and the results can be used to compensate for small perturbations in networks. The results are then applied to lossy reactive networks to compensate for the shifts in the natural frequencies due to the introduction of small losses.