## 1 Introduction  
The stable control of a mechanical system is paramount for safe operation. Many control techniques have been studied and researched to ensure the safe operation of diverse mechanical systems, especially aircraft systems. Aircraft control is a challenging task because of aerodynamic uncertainties. The aerodynamics govern the translational and rotational motion of an aircraft where the latter is more difficult to obtain than the former, imposing high uncertainty when implementing a controller. Care has been taken for the safe flight of aircraft using linear and nonlinear controllers which are constantly researched to this day. As an extension, this paper focuses on robust controller formulation for the rotational motion of an aircraft using incremental dynamics and nonlinear disturbance observers. Linear control methodologies, such as traditional proportional-integral-derivative (PID) control [1], linear quadratic regulator (LQR) [2], and H-Infinity technique [3], were introduced and applied to nonlinear systems before research on nonlinear control became mature. The nonlinear system needs to be transformed into linear counterparts using Taylor series expansion, linearizing the system at each operating point or state to use linear controllers, a method called gain scheduling [1, 4]. The problem with this approach is that as the number of operating states increases, the number of linearized systems also increases, mandating the need to increase the number of tuning processes because of linear controllers for each state. If the control specification is changed, all the linear controllers in every linearized point need to be re-tuned. A few sets of operating states may be used but since a linearized system represents the true nonlinear system only at the close range of state at the linearization, it is recommended to select many sets of linearization points to cover as much region of state space as possible to match the nonlinear system being controlled. Nonlinear control methodologies like feedback linearization-based nonlinear dynamic inversion (NDI) control [5] and backstepping [6], which have been developed and improved, have relieved the burden of gain scheduling required for linear controllers. To do so, nonlinear controllers, such as those based on diffeomorphic mapping functions, eliminate the need for gain scheduling by transforming systems into linear equivalents [7; 8]. The nonlinear controllers are especially useful to conventional fixed-wing aircrafts which eliminate the need for gain scheduling. [PERSON], [PERSON], and [PERSON] [9] showed that nonlinear controllers using diffeomorphic mapping are equivalent to linear controllers derived from linearized state transition systems using Taylor series expansion. This relationship indicates that nonlinear controllers could provide more cost-effective solutions compared to linear controllers, which explains their widespread use in military aircraft applications [10]. However, the reliability of the linear systems derived from diffeomorphic mapping heavily depends on the accuracy of the nonlinear system model [11]. If the uncertainties in the diffeomorphic mapping function increase from the true model, the performance of the nonlinear controllers may decrease and even fall into instability due to incorrect mapping. This poses a serious problem for the rotational flight control of aircraft as rotational aerodynamics are hard to acquire accurately. Incremental dynamics is a modification of nonlinear dynamics that is derived from the Taylor series expansion. The idea of incremental dynamics originated from [PERSON]'s research [12] and was later improved upon by [PERSON] [13]. Proposed to mitigate model dependency, the incremental dynamics involves directly using the state derivative. The nonlinear mapping function based on the incremental dynamics can be used to obtain linear dynamics where linear control methods can be used.