Part of the reactor design process is performance evaluation according to predefined criteria, including reactor stability behavior under different conditions. This work focuses on the stability characterization of a reactor system with feedback under low reactor power, low reactor coolant flow conditions. Such conditions might be encountered, for example, after a loss of flow without scram in some passively safe reactor designs. Algebraic and frequency stability-criteria-based methods are developed to find stability regions, stability boundary surface in system parameter space, and frequency of oscillation at oscillatory instability boundaries. Models are developed for the reactor, its detailed thermal-hydraulic reactivity feedback path associated with coolant outlet temperature, and decay heat. Developed stability analysis tools are applied to the system model. A unique aspect is the assessment of the influence of decay heat on stability. Other selected parameters are the following: temperature coefficient of reactivity, reactor coolant flow, and natural-circulation flow. The result is a stability boundary surface in four-dimensional system parameter space and its associated frequency of oscillation surface. Adopting model parameter values from two reactors results in system parameters within the stable region. Conditions for system parameters to remain in the stable region are identified.