Stabilization of perturbed integrator chains using Lyapunov-Based Homogeneous Controllers

2013/03/21 by Harmouche, Mohamed, Laghrouche, Salah, Chitour, Yacine
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1303.5330

Abstract

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 \citeLevant2001 is a particular case of our controller.

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