Abstract
This study is concerned with the finite-time synchronisation control (FTSC) of complex networks with discontinuous and continuous node dynamics. Two types of controllers (including continuous and discontinuous ones) are designed to ensure synchronisation of networks based on non-smooth analysis. Many sufficient criteria are given to guarantee FTSC by utilising the famous finite-time stability theorem. Compared the new obtained results with the previous literatures, the FTSC is discussed firstly when the node dynamics as well as the controllers are both discontinuous. Meanwhile, the upper bound of the settling time for synchronisation can be estimated. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results.