## 1 Introduction  
The performance indicators of aircraft, such as thrust weight ratio, economic efficiency and control performance, raise higher requirements for aircraft engines [1; 2; 3]. These requirements bring the need for more adjustable variables in the engines, which means the engine control system has multi-inputs and multi-outputs. Coupling inherently exists among these inputs and outputs. Moreover, the nonlinear characteristics of aircraft engines is another problem to be solved in its control design. This nonlinearity results from the engine thermodynamic characteristics and the variety of its initial and operating conditions. One can investigate the nonlinearity by a component-level thermodynamic model, what we called the nonlinear model. For the engine control design, most of the researchers build a linear model, such as a state space variable model (SSVM) based on the nonlinear model, which will cause modeling error during the linearization. The parameters in the SSVM may be disturbed by airflow distortion or other devices. At the same time, due to the mechanical manufacture and the assembly, there exists a difference between individual engines, which results in the parameter disturbance of the SSVM. All of these problems--couplings, nonlinearity, modeling errors, parameter perturbation and individual difference--present researchers with challenges on the control design for an aircraft turbofan. In order to conquer the mentioned problems in the aircraft engine control, researchers have been putting great efforts into the methods of robust control. The linear quadratic regulator (LQR) method has strong robustness and a simple structure, which was applied to the F100 aircraft engine and other linear systems [4; 5]. In the multivariable control of the F100, the LQR method was utilized to design the proportional part of the control. While the LQR method relies on a nominal linear system model and needs to know all of its states, if nonlinearity, uncertainty and modeling errors, which cause the remarkable mismatch between the dynamics of real systems and their models, exist, the characteristics of the LQR controller will deteriorate evidently. As was mentioned in [4], if the gain of LQR controller was not in the gain schedule, the system stability was unable to be guaranteed. To solve the problem that the LQR method cannot be utilized with the lack of partial states, the linear quadratic gaussian(LQG) method adopts the Kalman filter as a state observer to estimate the states and realize the state feedback control [6; 7]. However, the Kalman filter weakens the robustness. The simulation in [6] shows that since the engine dynamics changes significantly due to the low temperature reaction in the combustion process, the performance of the LQG controller becomes worse. In [7], for the dynamics of homogeneous charge compression ignition (HCCI) engines remains invariant, the robustness of the discrete-time LQG methods cannot be verified sufficiently. To enhance the robustness of the LQG method, the loop transfer recovery (LTR) design is added to achieve the LQG/LTR approach for a linear system [8; 9]. In [9], a non-full recovering LQG/LTR approach is applied to a turbofan engine. No uncertainty nor noise are considered in the controller design, and the system is actually a nominal system. The performance of the LQG/LTR controller is only validated at one operating condition, namely, \(H=0\) km, \(Ma=0\). When facing a complicatedly-varying dynamics, such as the dynamics of turbofan engines, the LQG/LTR controller may hardly recover the transfer function desired. The \(H_{\infty}\) control theory attracts many researchers in robust control design, especially in the noise elimination by setting a disturbance rejection level from noises to outputs. The research works in this field are numerous [10; 11; 12; 13].