Traditionally real-time systems and security have been considered as separate domains. Recent attacks on various systems with real-time properties have shown the need for a redesign of such systems to include security as a first class principle. In this paper, we propose a general model for capturing security constraints between tasks in a real-time system. This model is then used in conjunction with real-time scheduling algorithms to prevent the leakage of information via storage channels on implicitly shared resources. We expand upon a mechanism to enforce these constraints viz., cleaning up of shared resource state, and provide schedulability conditions based on fixed priority scheduling with both preemptive and non-preemptive tasks. We perform extensive evaluations, both theoretical and experimental, the latter on a hardware-in-the-loop simulator of an unmanned aerial vehicle (UAV) that executes on a demonstration platform.