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Future space missions will require onboard autonomy to reduce data, plan activities, and react appropriately to complex dynamic events. Software to support such behaviors is computationally-intensive but must execute with sufficient speed to accomplish mission goals. The limited processing resources onboard spacecraft must be split between the new software and required guidance, navigation, control, and communication tasks. To-date, control-related processes have been scheduled with fixed execution period, then autonomy processes are fit into remaining slack time slots. We propose the use of quality-of-service (QoS) negotiation to explicitly trade off the performance of all processing tasks, including those related to spacecraft control. We characterize controller performance based on exhaustive search and a Lyapunov optimization technique and present results that analytically predict worst-case performance degradation characteristics. The results are illustrated by application to a second-order linear system with a linear state feedback control law.