Corrigendum

This article refers to:

Certainty equivalence adaptation combined with super-twisting sliding-mode control

Barth, A., Reichhartinger, M., Wulff, K., Horn, M., & Reger, J. (2016). Certainty equivalence adaptation combined with super-twisting sliding-mode control. International Journal of Control, 89(6), 1767–1776.

When this article was first published online, the estimate for $2|z_1|{\dot{V}}_0$ preceeding (14) was incorrect. However, the claim ${\dot{V}}_0<0$ follows as a special case of Theorem 2 in Moreno and Osorio (2008) with ϱ₂ = 0 for k₁ > 2δ₁ and $k_2>\frac{k_1}{2}\frac{5k_1{\delta }_1+4{\delta }_1^2}{k_1-2{\delta }_1}$. Moreover, for k₁ > δ₁, k₂ > 0, the claim ${\dot{V}}_0<0$ can be verified by guaranteeing the existence of a common quadratic Lyapunov function for all $|a_2(x,t)|\le {\delta }_1{\left|\sigma \left(x\right)\right|}^{\frac{1}{2}}$, see Barth et al. (2017).