Stabilisation of perturbed chains of integrators using Lyapunov-based homogeneous controllers

In this paper, we present a Lyapunov-based homogeneous controller for the stabilisation of a perturbed chain of integrators of arbitrary order r ≥ 1. The proposed controller is based on homogeneous controller for stabilisation of pure chain of integrators. The control of homogeneity degree is also introduced and various controllers are designed using this concept, namely a bounded-controller with minimum amplitude of discontinuous control and a controller with globally fixed-time convergence. The performance of the controller is validated through simulations.