This paper presents an efficient robust control design approach for an air‐breathing engine for a supersonic vehicle using the Lyapunov stability theory based nonlinear backstepping control, augmented with unscented Kalman filter (UKF). The primary objective of the control design is to ensure that the thrust produced by the engine tracks the commanded thrust by regulating the fuel flow to the combustion chamber. Moreover, as the engine operates in a supersonic range, an important secondary objective is to manage the shock wave location in the intake for maximum pressure recovery with adequate safety margin by varying the throat area of the nozzle simultaneously. To estimate the states and parameters as well as to filter out the process and sensor noises, a UKF has been incorporated for robust output feedback control computation. Furthermore, independent control designs for the actuators have been carried out to assure satisfactory performance of the engine. Additionally, a guidance loop is designed to generate a typical flight trajectory of the representative vehicle using a nonlinear suboptimal input constrained model predictive static programming formulation for testing the performance of the engine. Simulation results clearly indicate quite successful robust performance of the engine during both climb and cruise phases.