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Cache systems are on-chip memory elements used to store data that are frequently referenced by programs. The advantage of storing data in cache, as compared to RAM, is that it has faster retrieval times, but it has the disadvantage of on-chip energy consumption. A cache-decay interval is the amount of time a cache element holds unreferenced data before being turned off (cleared). The choice of a cache-decay interval comprises a balance between low energy consumption and low induced miss rates. In certain applications this balance is determined off line by computing the cache-decay interval that would yield a given level of induced miss rates. However, the lack of precise models, coupled with program-dependent behavior of the cache system, result in possibly-drastic fluctuations in the induced miss rates for a given decay interval. This paper presents a control system designed to track a given reference of induced miss rates by recomputing (in real time) the decay interval. Simulation studies indicate that the plant can be approximated adequately by a power function. The controller's design is carried out in the log domain, where the system is linear but subjected to an unknown output disturbance. We propose an integral controller and perform its stability analysis. Simulation studies on Simplescalar, a microprocessor simulator, testify to the efficacy of our proposed approach and appear to yield tighter bounds than those derived to-date by other means.