In this paper, we present a Lyapunov-based homogeneous controller for the stabilization of a perturbed chain of integrators of arbitrary order r≥1. The proposed controller is based on homogeneous controller for stabilization of pure integrator chains. The advantages to control the homogeneity degree of the controller are also discussed. A bounded-controller with minimum amplitude of discontinuous control and a controller with fixed-time convergence are synthesized, using control of homogeneity degree, and their performances are shown in simulations. It is demonstrated that the homogeneous arbitrary HOSM controller \cite{Levant2001} is a particular case of our controller.
@article{arxiv.1303.5330,
title = {Stabilization of perturbed integrator chains using Lyapunov-Based Homogeneous Controllers},
author = {Mohamed Harmouche and Salah Laghrouche and Yacine Chitour},
journal= {arXiv preprint arXiv:1303.5330},
year = {2014}
}