State Equations of Electrical Networks from a Lagrangian Formulation

This correspondence presents a systematic method of obtaining the state equations for lumped linear bilateral electrical networks using energy-state functions and Lagrange´s equation. By applying a specified set of holonomic constraint equations in addition to a Legendre transformation on a portion of the system energy-state function, modified Lagrangian and Rayleigh functions are formulated, which, when substituted into Lagrange´s equation, yield equations of state with capacitor tree voltages and inductor link currents as state variables. An example is included to illustrate the procedure.