AbstractIn allusion to the multi‐variable robust control for the turbofan engine with the large envelope, an almost output regulation (AOR) problem is discussed for a class of turbofan switched systems under multi‐source disturbances and time delay. The addressed disturbances include the regulated disturbance signal, the modeled disturbance from the input channel and the energy‐bounded disturbance. First of all, a disturbance observer is constructed to estimate the unknown disturbance in the system input. Then, by combining the output regulation method and the disturbance observer‐based control (DOBC) method, a switched composite regulation controller is developed to deal with the AOR problem of the turbofan switched systems and reject the adverse effects of disturbances. Through the multiple Lyapunov function method, a set of sufficient conditions are obtained to guarantee the AOR property with the performance and disturbance suppression ability. Finally, the validity of the proposed method is demonstrated by applying the composite anti‐disturbance regulator to the regulation of the speed and pressure ratio for the turbofan model.