Robustness of finite-time stability property for sliding modes

The paper is devoted to analysis of robustness of the finite-time stability property for discontinuous systems using the homogeneity framework. A short introduction into sliding-mode systems, homogeneity and finite-time stability is given. The main result connects the homogeneity degree of a discontinuous system and its type of robust stability. For robustness analysis the input-to-state stability method is used. The proposed theory is applied to a series of well known sliding-mode control algorithms.