This paper provides stability analysis for phase shifting active combustion control system where modulation of the fuel flow is used to suppress thermo-acoustic instability. The analysis is based on Krylov-Bogolubov averaged model for the oscillations with the external periodic forcing. The amplitude dynamics and phase dynamics are described by nonlinear first order models. The control inputs are the amplitude and phase of forcing (fuel modulation). The analysis demonstrates that phase dynamics and amplitude dynamics are each unstable in the desired target regime. Practical stabilizing control approaches and their limitations in the presence of feedback delays are discussed and analyzed. The analysis in this paper is verified in detailed simulations and validated in experiments with a jet engine scale combustor rig.