Elimination of zero eigenvalues from the A matrix for linear RLC networks

Abstract

This correspondence deals with the elimination of zero eigenvalues of the A matrix for linear time-invariant RLC networks and the consequent reduction of order of the state equations. The state variables used are a subset of the capacitor voltages and inductor currents, chosen such that the order of the state equation is equal to the number of finite nonzero eigenvalues or natural frequencies of the network. Two methods are given for the reduction to minimum order of the commonly used linear state equation.