A control approach for practical and asymptotic stabilization of driftless controllable control systems with perturbations is proposed. This type of systems naturally appears when addressing the trajectory stabilization problem of driftless control systems on Lie groups. The objective of the approach is to provide practical stability whatever the perturbation ---e.g. practical stability of any trajectory in the state space---, and asymptotic stability or convergence to zero of the error variables when the perturbation term is zero or tends to zero. A general framework is presented in this paper and a control solution is proposed for the class of chained systems.