Although some existing multiprocessor energy-efficient approaches for periodic real-time tasks can achieve more energy savings with taking practical overhead of processor into consideration, they cannot guarantee the optimal feasibility of periodic tasks. For the non-ignorable overhead of switching the processor state in embedded real-time systems, this paper proposes an overhead-aware online energy-efficient real-time scheduling algorithm in multiprocessor systems, the periodic tasks with largest utilization first based on switching overhead (PLUFS). PLUFS utilizes the fluid scheduling concept of time local (TL) remaining execution plane and the switching overhead of the processor states to implement energy-efficient scheduling for real-time tasks in multiprocessors at the initial time of each TL plane as well as at the end execution time of a periodic task in each TL plane. Consequently, PLUFS can obtain a reasonable tradeoff between the real-time constraint and the energy-saving while realizing the optimal feasibility of periodic tasks. Mathematical proof and extensive simulation results demonstrate that PLUFS guarantees the optimal feasibility of periodic tasks, and on average saves more energy than existing algorithms, and improves the saved energy of some existing algorithms by about 10% to 20% at the same time.