## 1 Introduction  
Electric energy demand is increasing everyday; thus, electric power engineers must pay special attention to the new grid topologies, including emerging technologies focused on the generation tasks. In this context, transient stability analysis is a critical stage in any power system where the Synchronous Generator (SG) is a key component for the dynamic performance [1]. Due to the power system's complexity, it is important to delimit the phenomena under analysis considering the time scales, where these dynamics are presented. The problem of power system stability is known by the power system community regarding the classification discussed in [1, 2, 3]. In [3], the definition and classification of power system stability, including the new relevant dynamic phenomena, have been revised. Transient stability as a part of rotor angle stability is recognized as a desirable study in power systems. A review of some important aspects on the damping of power system oscillations is presented in [4]. Important strategies are reviewed and compared among them to define some criteria to evaluate their performance in the face of the challenges of modern electric power systems. Robust control strategies are an important alternative for generation units [5]. High-performance control design of multi-input and multi-output nonlinear interconnected electric power systems demands accurate mathematical models and knowledge of the physical parameters [6, 7], especially when a large operational range is needed. Important control strategies for the synchronous generator in power systems, covering linear, nonlinear and adaptive approaches have been proposed. However, the power system might confront complex phenomena that could cause failure on the control algorithms if these phenomena are not considered as included in the design stage. In that sense, nonlinear controllers for stabilization and synchronization of interconnected synchronous generators emerge as an alternative solution. In [8], a Proportional-Integral-Derivative (PID) linear scheme, combined with a Non-Linear Threshold Accepting Algorithm (NLTA), is used to design a robust strategy that combines an Automatic Voltage Regulator and a Load Frequency Control (AVR-LFC) for a multi-area power system. The results after several trials show the ability of the NLTA to adjust its performance under different operating scenarios and improve the transient responses. On the other hand, a fractional-order sliding mode controller for the stability of a multimachine power system is proposed in [9]. This controller is used to make the power system stable in a fixed time, independent of the initial operating conditions. The proposal to regulate the excitation of the synchronous generators improves the transient stability of the power system by reducing the chattering phenomena and ensuring the power system stabilization in an upper bound time. This enhances the dynamic performance of the power system. In [10], a control strategy for the interconnected power system is proposed. The design procedure requires three stages--observer, fractional sliding mode surface and controller--but the procedure requires the definition of several considerations to guarantee the expected performance. Moreover, model uncertainty and unknown external dynamic disturbances represent challenging issues that should be considered in the robust and efficient planned motion tracking control design problem for complex practical nonlinear dynamic systems. In this sense, a control approach based on the backstepping control design methodology and adaptive Neural Networks for a wheelchair upper-limb exoskeleton robot system is introduced in [11]. Furthermore, in [12] sliding modes and adaptive Neural Networks have been properly combined for developing a fixed-time position tracking control method for a wheelchair upper-limb exoskeleton robot system subjected to exogenous disturbances.