Formulation of equations in terms of scalar functions for lumped non-linear networks

A general method is presented of formulating the Lagrangian and anti-Lagrangian equations for networks consisting of non-linear RLCM (M = memristor) multiports with hybrid representation. The formulation is obtained with no restriction on the network topology. An explicit procedure is given to construct the scalar functions needed. This procedure is based on the concept of L and H functions introduced. The Brayton-Moser equations in a generalized form can be directly obtained from the anti-Lagrangian equations. From these equations, new equations of Brayton-Moser type can also be derived. The invariance property of Lagrangian and anti-Lagrangian equations under a transformation of variables is also discussed.