In a previous work, we have proposed a way, founded on the ‘reactive energy minimization principle’, for improving the accuracy of Kochenburger's method in the study of non-linear systems. We prove, here, the convergence of this algorithm. In order to do so, we prove firstly, with the help of Tsypkin's theory that the algorithm is exact for on-off closed-loop systems. From this result and by using some theorems on functional continuity which have been established elsewhere, we prove that the proposition is still true, for a greater set of systems.