  In this paper, a variable gain super-twisting algorithm based on a barrier
function is proposed for a class of first order disturbed systems with
uncertain control coefficient and whose disturbances derivatives are bounded
but they are unknown. The specific feature of this algorithm is that it can
ensure the convergence of the output variable and maintain it in a predefined
neighborhood of zero independent of the upper bound of the disturbances
derivatives. Moreover, thanks to the structure of the barrier function, it
forces the gain to decrease together with the output variable which yields the
non-overestimation of the control gain.
