Global feedback stabilisation of lower-triangular nonlinear systems in any prescribed finite time

Abstract

In this paper, global state feedback and output feedback stabilisation problems are considered for a class of time-varying lower-triangular nonlinear systems in any prescribed finite time. The nonlinear terms admit an incremental rate depending on a time-varying continuous function. Firstly, by introducing a novel state transformation consisting of a time-varying gain and a scaling of the state by a function of time that grows unbounded towards the terminal time, the involved system is transformed into a new one easily designing a feedback controller. Then based on the Lyapunov theorem and choosing the time-varying gain, both state feedback and output feedback controllers are constructed respectively to globally stabilise the new system in the scaled state representation, yielding the global feedback stabilisation in any prescribed finite time of the involved system. Simulation examples are given to demonstrate the effectiveness of the proposed control strategies.