Component-based software systems with real-time requirements are often scheduled using processor reservation techniques. Such techniques have mainly evolved around hard real-time systems in which worst-case resource demands are considered for the reservations. In soft real-time systems, reserv- ing the processors based on the worst-case demands results in unnecessary over-allocations. In this paper, targeting soft real-time systems running on multiprocessor platforms, we focus on components for which processor demand varies during run-time. We propose a feedback scheduling framework where processor reservations are used for scheduling components. The reservation bandwidths as well as the reservation periods are adapted using MIMO LQR controllers. We provide an allocation mechanism for distributing components over processors. The proposed framework is implemented in the TrueTime simulation tool for system identification. We use a case study to investigate the performance of our framework in the simulation tool. Finally, the framework is implemented in the Linux kernel for practical evaluations. The evaluation results suggest that the framework can efficiently adapt the reservation parameters during run-time by imposing negligible overhead.