In order to obtain desired steady-state and transient performance of a gas turbine aero-engine during its operation, a usual way is to control the engine to operate in a manner close to its physical limits. The thermodynamic performance of a gas turbine aero-engine varies greatly within a wide working envelope, affected by factors such as engine performance degradation, actuator response lag and combustion time-delay. When the engine works in extreme conditions, for example rapid acceleration, some phenomena such as over-speed, over-temperature and over-pressure may occur. For this reason, various restrictions are often set in the engine control system to ensure safety during its operation, which are often realized by the form of saturation. In this paper, a compensation structure for gas turbine aero-engine state time-delay and input saturation is proposed. At first, the problems frequently occurred in the gas turbine aero-engine control system are investigated. And the gas turbine aero-engine control model is derived based on a thermodynamic non-linear model and its linearization model is established, together with its designed compensation structure. Differing from the existing technologies, a combination of dynamic system input saturation feedback and static state time-delay feedback is adopted in the proposed model. Then, the saturated nonlinearity and time-delay characteristic are introduced as convex combinations in the stability analysis. The local stability conditions of the closed-loop system are obtained by using Lyapunov–Krasovskii functionals and linear matrix inequalities (LMIs). Finally, hardware-in-loop (HIL) experiments are conducted to verify the feasibility of the proposed compensation method.