Parameter preference for the continuous super-twisting-like algorithm based on H∞ norm analysis

In variable structured systems, plenty of designs are built to be homogeneous. Such unperturbed homogeneous dynamics with negative homogeneous degree guarantee finite time convergence. Previous studies provide lower bounds for parameters that result in such finite-time convergence property. In this paper, we propose a new perspective on parameter preference, based on H∞ norm analysis. Contrary to other studies, which propose such norm non-homogeneous or homogeneous, yet of non-zero degree, we build a homogeneous H∞ norm of homogeneous degree zero, thus global and constant. Based on data collected of this norm on the continuous super-twisting-like algorithm, we give recommendations for choosing the parameters.