Active control using periodic fuel injection has the potential of suppressing combustion instability without radically changing the engine design or sacrificing performance. A study is carried out of optimal model-based control of combustion instability using fuel injection. The model developed is physically based and includes the acoustics, the heat-release dynamics, their coupling, and the injection dynamics. A heat-release model with fluctuations in the flame surface area, as well as in the equivalence ratio, is derived. It is shown that area fluctuations coupled with the velocity fluctuations drive longitudinal modes to resonance caused by phase-lag dynamics, whereas equivalence ratio fluctuations can destabilize both longitudinal and bulk modes caused by time-delay dynamics. Comparisons are made between the model predictions and several experimental rigs. The dynamics of proportional and two-position (on-off) fuel injectors are included in the model. When the overall model is used, two different control designs are proposed. The first is an linear quadratic Gaussian/loop transfer recovery controller, where the time-delay effect is ignored, and the second is a positive forecast controller, which explicitly accounts for the delay. Injection at 1) the burning zone and 2) farther upstream is considered. The characteristics of fuel injectors including bandwidth, authority (pulsed-fuel flow rate), and whether it applies a proportional or a two-position (on-off) injection are discussed. We show that increasing authority and increasing bandwidth result in improved performance. Injection at location 2 compared to location 1 results in a tradeoff between improved mixing and increased time delay. It is also noted that proportional injection is more successful than on-off injection because the former can modulate both amplitude and phase of the control fuel.