A robust multi-period model is proposed to minimize the energy consumption of IP networks, while guaranteeing the satisfaction of uncertain traffic demands. Energy savings are achieved by putting into sleep mode cards and chassis. The study of the solution robustness shows that there is a trade-off between energy consumption and the solutions conservatism degree. The model allows this trade-off to be tuned by simply modifying a single parameter per link. The multi-period optimization is constrained by inter-period limitations necessary to guarantee network stability. Both, exact and heuristic methods are proposed. Results show that up to 60% of the energy savings can be achieved for realistic test scenarios in networks operated with flow-based routing protocols (i.e. MPLS) and with a good level of robustness to traffic variations.