###### Abstract
On the other hand, inversion-based and stable inversion approaches are completely dependent on accurately determined system models and they are susceptible to the closed-loop system instability problem in the case of perturbation of external disturbances [15; 16]. Finally, the pole-zero cancellation-based approaches such as the real-zero elimination approach led to creating a non-causal controller and hence internally unstable systems [17; 18]. These limitations are the impetus for the proposed method, which can ensure the internal stability, robustness, and a desirable performance in dealing with NMP dynamics by means of transforming the NMP to minimum-phase dynamics using the fractional-order control for the first time then using the existing powerful linear control techniques such as the proportional-integral-derivative (PID) controller, H2, H\({}_{\infty}\), and linear quadratic regulator (LQR) optimal control. Therefore, the main advantage of the proposed approach is the reliance on the classical feedback control to obtain a robust and high performance as well as internal stability against NMP dynamics. It can be concluded that the main differences between the proposed approach and the existed methods in literature that essentially rely on transforming the non-minimum phase to minimum phase dynamics are:  
1. Compared with the input state FBL method, which is based on adding hard constraints such as the second-order Lyapunov constraint to ensure the closed-loop stability in the case of NMP dynamics [19], the proposed method ensures a robust and stable closed-loop for the NMP dynamics with actuator faults without any additional constraints. 2. In contrast with the real-zero elimination, which can be applied only with MIMO systems [10], the proposed method is appropriate for both MIMO and SISO systems without necessitating to reach all the internal states. Generally, the linear quadratic regulator (LQR), which is based on the optimal control theory, offers more significant advantages than the classical control methods with respect to time response performance, control effort, robustness for uncertainty, and disturbance and noise rejection capabilities [20; 21]. As reported in the literature, the LQR controller has been successfully applied to deal with various types of NMP dynamics, for instance, m-link robotic manipulators [22], phase electrohydraulic systems (EHS) [23], and wheeled bipedal robot with kinematic loops [24]. It is remarkable that the first significant application of multivariable control based on the linear quadratic regulator (LQR) started in the Boeing company (Chicago, IL, USA) in 1978 as a part of NASA's research programs [25]. In their work, the LQR theory was applied as a second option for repeated attempts based on classical synthesis techniques to improve the control of heading- and track-hold functions of autopilot developed for the Boeing 767 commercial transport airplane. Furthermore, the LQR and linear quadratic gaussian (LQG) design approaches have been implemented for more than 20 years in the autopilots of Boeing aircraft [26]. As an example, the work in [27] focused on the design of a high-performance control of longitudinal dynamics of a highly flexible aircraft (HFA), where integral reinforcement learning (IRL) and LQR were combined to constitute an adaptive online data-driven tracking controller. The data were collected within an expected time interval using the IRL technique, and then the LQR utilized these data to calculate the optimal feedback gains. The LQR has been introduced with other control strategies to manage the aircraft's non-minimum phase nature. In [28], a quantitative feedback theory (QFT) was proposed and compared with the LQR control approach to solve the non-minimum phase problem of the longitudinal model of hypersonic aircraft and hence a robust controller was designed against the uncertainty problem of large aerodynamic parameters due to complex flight environments.