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In this paper, a variable gain super-twisting algorithm based on a barrierfunction is proposed for a class of first order disturbed systems withuncertain control coefficient and whose disturbances derivatives are boundedbut they are unknown. The specific feature of this algorithm is that it canensure the convergence of the output variable and maintain it in a predefinedneighborhood of zero independent of the upper bound of the disturbancesderivatives. Moreover, thanks to the structure of the barrier function, itforces the gain to decrease together with the output variable which yields thenon-overestimation of the control gain.

Barrier function-Based Variable Gain Super-Twisting Controller