Combustion instability is a major issue in design of gas turbine combustors for efficient operation with low emissions. A transfer matrix-based approach is developed in this work for the stability analysis of gas turbine combustors. By viewing the combustor cavity as a one-dimensional acoustic system with a side branch, the heat source located inside the cavity can be described as the input to the system. The combustion process is modeled as a closed-loop feedback system, which enables utilization of well-established classic control theories for the stability analysis. Due to the inherent advantage of the transfer matrix method and control system representation, modeling and analysis of the system becomes a straightforward task even for a combustor of the complex geometry. The approach is applied to the stability analysis of a simple combustion system to demonstrate its validity and effectiveness.