Prescribed-time stabilisation design for a class of nonlinear systems with state constraints

This paper will investigate the prescribed-time stabilisation problem for a class of nonlinear systems with state constraints. A recursive design algorithm is proposed to solve the prescribed-time stabilisation problem. Firstly, a barrier Lyapunov function (BLF) is employed and a time-varying coordinate transformation is utilised. Then, a modified method of LgV-backstepping is proposed, and a novel stabilising function by adding a fractional term proposed in this paper which is capable of decreasing the BLF to the origin within any desired settling time and then achieving the prescribed-time stabilisation. Such a fractional term plays an important role in achieving prescribed-time stabilisation. Next, the analysis of the prescribed-time stabilisation with state constraints is presented. Finally, an example shows the effectiveness of the proposed method. The feature of this paper is that the settling time is not only independent of the design parameters, nor does it depend on the initial conditions, and can be set according to per our will. Other is that the constraints of all the states are not violated.