Robust finite time stability and stabilisation: A survey of continuous and discontinuous paradigms

The aim of this paper is to provide a survey of the tools for analysis and synthesis of finite time stable controllers. The paper analyses the literature in continuous and discontinuous finite time stabilisation in a unified way covering both the fundamentals as well as the latest techniques available in this non-linear control paradigm. The contribution of the paper lies in its exposition of the robustness properties that continuous and discontinuous controllers guarantee. Some open problems are identified which are relevant to both the theory and practice of finite time stabilisation.