Most mobile robot navigation techniques that depend on reference RF beacons rely on approximating line-of-sight (LOS) distances between these beacons and the robot. The approximation of LOS is mostly performed using received signal strength (RSS) measurements of signals propagating between the robot and RF beacons. However, to date, relying on RSS measurements for approximating LOS distance remains a significant challenge. Accurate mapping between RSS measurements and LOS distance is almost impossible to achieve in an indoor reverberant environment. In this paper, we design a partially-observed feedback controller for a differential drive mobile robot (DDMR) where the feedback signal is in the form of noisy RSS measurements emitted from radio frequency identification (RFID) tags placed in the environment. The proposed controller does not require an accurate mapping between the LOS distance and the RSS measurements from RFID tags. In addition, it takes into account the robot's actuator (speed) constraints. Unlike many other previously devised solutions, the proposed control scheme does not require the linearization of the nonlinear DDMR model. The performance of this method is demonstrated through both numerical simulations and real-time experiments.