For a class of switched linear systems, we propose a switching strategy that combines time-driven switching with event-driven switching. This switching strategy not only makes the switched systems stable, but also reduces the switching frequency in contrast with the existing switching laws. In addition, the switching law is robust against (time-varying and nonlinear) system perturbations. We prove that, under this switching law, the perturbed systems are bounded for bounded perturbations, convergent for convergent perturbations, and exponentially convergent for exponentially convergent perturbations. For switched linear systems with measured outputs, we also develop an observer-based switching strategy which robustly stabilizes the perturbed systems.