  In this paper, we present a Lyapunov-based homogeneous controller for the
stabilization of a perturbed chain of integrators of arbitrary order $r\geq 1$.
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.

Optimization and Control