Fixed-time stabilisation and consensus of non-holonomic systems

This study deals with the fixed-time stabilisation of a class of non-linear systems. A non-linear controller, based on sliding mode, is proposed to ensure the fixed-time stabilisation of a non-holonomic system in chained form. An upper bound of the settling time, independent of the initial system state, is estimated. Then, a distributed switched strategy, based on local information, is introduced to solve the fixed-time consensus problem for multiple non-holonomic agents. Using Lyapunov functions, the switching times are explicitly given and only depend on the controller gains and the Laplacian matrix. Simulation results highlight the efficiency of the proposed method.