3D integration enables building caches from different types of technologies such as SRAM, Magnetic RAM (MRAM), DRAM, and Phase-change RAM (PRAM). Hybrid cache architectures (HCAs) have been proposed to take advantage of the benefits offered by these types of technologies. Employing this novel cache architecture to build shared caches in chip multiprocessors (CMPs) can lead to significant performance and power consumption improvements. In this paper, we focus on a 3D CMP design in which the shared last level L2 cache is composed of an MRAM layer and an SRAM layer stacked upon the processing cores and present a control theory centric approach designed to partition this shared hybrid L2 cache space dynamically among concurrently running applications in order to satisfy the application-level performance QoS targets. At each time interval, the two layers of the hybrid L2 cache are partitioned, based on the cache demands made by the controllers of the applications, to satisfy the specified performance targets. We evaluate our feedback control based scheme using various workloads. Our experimental evaluation shows that the proposed scheme is able to satisfy the specified performance QoS in most of the tested cases, by partitioning the hybrid cache space of the 3D CMP among co-runner applications.