Homogeneous Time-Varying Systems: Robustness Analysis

The problem of stability robustness with respect to time-varying perturbations of a given frequency spectrum is studied applying homogeneity framework. The notion of finite-time stability over time intervals of finite length, i.e., short-finite-time stability, is introduced and used for that purpose. The results are applied to analyze the Super-Twisting Algorithm (STA) behavior under time-varying perturbations. Some simulation examples illustrate these robustness properties.