Power based modeling and stabilization of telegraphers equations

This paper works out the idea of Brayton and Moser towards Telegraphers equations. The idea of power based modeling is established by building a mixed potential function which subsumes the dynamics of a transmission line system. The main belief in writing this paper is for continuing the theory of mixed potential function in relation to power shaping of such complex circuits. The Inducement of nonlinear elements in the circuit may lead to the ultimate issues of stability, due to these dynamics in the circuit they tend to have more complex behavior and exotic to instability. This nature of the circuit lets this paper illustrate the BM modelling and control law. The approach of mixed potential function for nonlinear circuits projects it to a special form of differential equations. This mixed potential function can be further used to prove the stability of circuits under certain conditions, by using theorems developed by Brayton and Moser. A mathematical derivation for the telegraph equation in terms of voltage and current for a section of a transmission line will be investigated with the help of current potential and voltage potential, the form for voltage potential and current potential in the telegraphic equations are explicitly and analytically derived.