In this paper, we address some robustness issues for a class of switched linear systems with non-linear perturbations. We illustrate through an example that the well-known state-space-partition-based switching law may lead to chattering in the event that the systems undergo perturbations. To overcome this, we propose a state-feedback switching law with a non-zero level set. We prove that this switching law can prevent the system from chattering. In addition, this switching law makes the perturbed systems bounded with bounded perturbations, and practically convergent with convergent perturbations. We also propose an observer-based switching law to steer the switched system stable with nice robustness performances.