## 1 Introduction
[12] developed a robust controller by integrating a sliding mode control (\(SMC\)) approach with a backstepping controller. The backstepping control scheme eliminates the chattering and oscillation issues typically associated with (\(SMC\)), and the resulting controller is capable of providing excellent reference tracking dynamics for both the pitch and yaw angles, even when accounting for parametric model uncertainties. A control scheme established on active disturbance rejection control and input shaping was proposed in [13] for the \(TRMS\). The control objectives involved accurately following the desired trajectories and ensuring disturbance rejection in both the horizontal and vertical planes. Additionally, the composite control demonstrated robustness against changes in system parameters, including variations in the natural frequency and damping ratio. In [14], two robust \(SISO\) fractional-order regulators (\(FO-PID\)) were proposed, in which the control of the pitch angle is completely independent from the control of the yaw angle. A fractional order integral-proportional derivative (\(FOI-PD\)) controller was simulated and trialed to control each rotor of the \(TRMS\) in [15]. The approach achieved enhanced disturbance rejection compared to the standard proportional integral derivative (\(PID\)) controller and proportional derivative (\(PD\)) controller. The controller parameters were optimized using the MATLAB(r) function fmincom. A robust \(2-DOF\) controller was proposed in [16] for the \(TRMS\), which had been previously separated into two \(SISO\) systems. This controller contains a fractional-order precompensator to ensure accurate reference path tracking behavior and a fractional post-compensator to enhance the closed-loop robustness. The adaptive explicit nonlinear model predictive control (\(AENMPC\)) method introduced in [17] was applied to the \(TRMS\) considering a strongly coupled nonlinear \(MIMO\) system with uncertain parameters. This approach provides improved control outcomes, including enhanced tracking performance, a smoother control law, and increased energy efficiency. More recently, a combination of proportional integral and proportional-derivative (\(PI-PD\)) controllers was proposed [18] for \(TRMS\), to control the pitch and yaw angles. Flight systems often experience delays, which can result from various factors, including high-order rotor response, control actuator dynamics, filtering processes, and computational delays [19]. Similarly, for \(TRMS\) flight systems that contain the time delay produced by the collection of sensor data [20] or that resulting from the cascading of multiple dynamic components used in the complex system [21], the design of the controller for the flight system becomes a big challenge. All of the above are grouped in what is denoted hardware-induced delays \(HID\). Moreover, an additional delay is produced when the \(TRMS\) is operated in teleoperated mode. Recent studies in the literature propose controller designs that tackle time delays in flight control, utilizing advanced adaptive control theory, such as integrating the Smith predictor with adaptive controllers [20], adaptive compensators based on observers [22], \(H_{\infty}\) controllers, adaptive podcast controllers [23], and robust adaptive controllers [24]. In these investigations, the degradation of the flying quality due to the time delay of the systems is considered, and the difficulty in controlling them is apparent. Persistent disturbances such as wind introduce errors in the position and orientation of \(TRMS\)s [13]. Controllers designed not only for positioning and orientation but also for disturbance rejection tend to be more complex to tune [25], and the inherent time delay of the \(TRMS\) often leads to control failures [21; 26]. To address these challenges, we aim to design a robust controller capable of mitigating the effects of disturbances and compensating for time delays.