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Consumer electronics platforms are progressively being introduced in most domains, from personal appliances to high-quality multimedia control infrastructures. They are high quality platforms that require that computation resources be used in a cost-effective way. Multimedia applications compete for resources in a greedy manner, which may threaten the safe system execution. Arbitration of application execution is needed to keep system stability, especially in the event of unexpected changes in the resource requirements demanded by applications. Changes may be caused by a modification in the nature of the incoming media or by the user action. Such changes should trigger an adaptation process to handle the new situation in a way that overall system quality is preserved. This paper describes the mechanisms that have been developed to handle situation where adaptation is needed in such a way that stability is preserved avoiding over reaction. An adaptation protocol based on the definition of a safety band for filtering peaks in resource demands is set for this purpose. The paper presents experimental results that show the appropriate filtering of these peaks, which validate the presented concepts.