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A power-down system has an on-state, an off-state, and a finite or infinite number of intermediate states. In the off-state, the system uses no energy and in the on-state energy it is used fully. Intermediate states consume only some fraction of energy but switching back to the on-state comes at a cost. Previous work has mainly focused on asymptotic results for systems with a large number of states. In contrast, the authors study problems with a few states as well as systems with one continuous state. Such systems play a role in energy-efficiency for information technology but are especially important in the management of renewable energy. The authors analyze power-down problems in the framework of online competitive analysis as to obtain performance guarantees in the absence of reliable forecasting. In a discrete case, the authors give detailed results for the case of three and five states, which corresponds to a system with on-off states and three additional intermediate states "power save", "suspend", and "hibernate". The authors use a novel balancing technique to obtain optimally competitive solutions. With this, the authors show that the overall best competitive ratio for three-state systems is 9 5 and the authors obtain optimal ratios for various five state systems. For the continuous case, the authors develop various strategies, namely linear, optimal-following, progressive and exponential. The authors show that the best competitive strategies are those that follow the offline schedule in an accelerated manner. Strategy "progressive" consistently produces competitive ratios significantly better than 2.

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