A generalization of Brayton-Moser´s mixed potential function

In this paper we give algorithms for constructing the Brayton-Moser´s mixed potential function for a class of nonlinear reciprocal RLC networks, and we state necessary conditions for their existence. We have attempted to find the largest possible class of networks for which such a scalar function of state variables consisting of capacitor voltages and inductor currents can be constructed explicitly. Our results are applicable to a certain subclass of complete networks. From a mathematical point of view, we show that the corresponding network equations belong to the class of index I systems