Predefined-time stabilisation of a class of nonholonomic systems

This paper deals with the predefined-time stabilisation problem for a class of uncertain chained-form nonholonomic systems. Based on a novel generalised Lyapunov-like characterisation of predefined-time stability, new predefined-time controllers are introduced for a class of first and second order systems with matched perturbations. Contrary to existing finite-time and fixed-time schemes, an upper bound of the settling time is an easily tuneable control parameter. Then, these results for first and second order systems are used to design a switching strategy, which guarantees the predefined-time stability of the closed-loop system. The switching time and the settling-time can be easily tuned according to the control parameters. A benchmark example is presented to show the effectiveness of the proposed method.