Self-synchronising grid-tied inverters use the internal dynamic states of their current regulator to estimate the voltage at the point-of-common-coupling (PCC), and then synchronise to this voltage estimate using a phase-locked-loop (PLL). This approach offers several benefits including a reduction in the required sensor count and improved harmonic attenuation. However, a self-synchronising control system is non-linear because the current regulator and PLL interact dynamically, which makes the analysis of the controller stability and sensitivity more difficult to quantify. This paper presents a linearized small signal model for a self-synchronising inverter that fully accounts for the current regulator and PLL dynamic interactions. This allows the stability of the inverter control loop to be assessed across a wide range of operating conditions. The model has been validated using detailed switched simulations of a three-phase grid-tied inverter, and tests conducted on a matching experimental inverter.