Abstract In aircraft propulsion as well as stationary power generation, gas turbine engines remain a key energy conversion technology due to their high thermal efficiencies and low emissions. However, as emission requirements become increasingly stringent, engine manufacturers have sought to design combustion systems that operate near the fuel-lean limit of flammability. In this study, superadiabatic matrix-stabilized combustion, also known as porous media combustion, is evaluated as an advanced combustion concept for extending the lean flammability limit to achieve improved efficiency and emissions. To this end, a Brayton cycle analysis is developed and key parameters of the porous matrix are identified for maximizing the extension of the lean flammability limit. It is shown that stabilization of combustion below the nominal lean flammability limit allows for the design of engines with significantly higher pressure ratios and lower dilution ratios without increasing turbine inlet temperatures, thus improving cycle thermal efficiency. Combustor flammability limits were shown to be extendable by up to 32% when employing matrix-stabilized combustion, resulting in thermal efficiency gains of up to 11% compared to a nominal design.