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In this paper, we present a power-conscious algorithm for jointly scheduling multi-rate periodic task graphs and aperiodic tasks in distributed real-time embedded systems. While the periodic task graphs have hard deadlines, the aperiodic tasks can have either hard or soft deadlines. Periodic task graphs are first scheduled statically. Slots are created in this static schedule to accommodate hard aperiodic tasks. Soft aperiodic tasks are scheduled dynamically with an on-line scheduler. Flexibility is introduced into the static schedule and optimized to allow the on-line scheduler to make dynamic modifications to the static schedule. This helps minimize the response times of soft aperiodic tasks through both resource reclaiming and slack stealing. Of course, the validity of the static schedule is maintained. The on-line scheduler also employs dynamic voltage scaling and power management to obtain a power-efficient schedule. Experimental results show that the flexibility introduced into the static schedule helps improve the response times of soft aperiodic tasks by up to 43%. Dynamic voltage scaling and power management reduce power by up to 68%. The scheme in which the static schedule is allowed to be flexible achieves up to 3.2% more power saving compared to the scheme in which no flexibility is allowed, when both schemes are power-conscious. Our work gives an average architecture price saving of 30% over a previous approach for embedded system architectures synthesized with execution slots for hard aperiodic tasks present.