We consider a resource synthesis technique for real-time systems where the energy budget is limited and the performance of the system depends on how resources and energy are used. We consider two performance models for a task: (1) a task has variable execution time and performance of a task depends on the amount of execution time received, and (2) the execution time of a task is constant and the performance of a task depends on its frequency. We first propose an optimal resource synthesis technique which maximizes system performance without energy constraints. We prove its optimality with the earliest deadline first (EDF) scheduling policy when the performance function of a task is non-decreasing and concave. We propose an energy-aware resource allocation technique for systems with energy constraints using the same analytical framework. The energy-aware resource synthesis technique considers both resource usage and energy consumption to find a near optimal solution that maximizes system performance within the energy budget.