On strict Lyapunov functions for some non-homogeneous super-twisting algorithms

In this paper strict, non-smooth Lyapunov functions for some non-homogeneous versions of the super-twisting algorithm are proposed. Convergence under the action of bounded perturbations for two basic forms of non-homogeneous algorithms will be studied by means of the Lyapunov functions. Since the homogeneity property cannot be used directly to prove stability of the algorithms, the availability of a Lyapunov function is of great importance for analysis and design in these cases. Moreover, exponential or finite-time and local or global stability are required to be established, since they are not derived from the homogeneity.