Some contributions to Lagrangian modelling of Power Converters

The paper explicitly shows that applying an EL model which keeps the inductor energy T = (1/2)Ls q̇L^2 while only making D and F depend on the switch u yields a state-space model that is valid for u=1 but incorrect for u=0 (it spuriously enforces Ls q̈L = −Rs q̇L) . It then constructs the correct, mode-wise assembled u-dependent energies T = (1/2)Ls(u q̇L)^2 and D = (1/2)[(u q̇L)^2 Rs + (u q̇L − q̇C)^2 R], obtaining a descriptor form with mass matrix diag(u,1) and emphasizing that one must not cancel u when u=0 . The paper further argues that, with proper labeling of generalized current coordinates, Kirchhoff constraints can be absorbed without an explicit constraint matrix A (unconstrained EL) , illustrated by multi-loop examples . The candidate solution reproduces these steps essentially verbatim: it (i) demonstrates the failure of the u-ignorant kinetic energy in the OFF mode, (ii) assembles the mode-wise data into T, V, D, F with explicit u-dependence to derive the same descriptor system and explains why the u factor on the derivative side must remain, and (iii) explains how choosing generalized current coordinates removes explicit constraints. It adds a brief comment on impulsive terms at switching, consistent with the framework though not discussed in the paper. Hence both are correct and the proofs are substantially the same.