## 1 Introduction
In [26; 27], a model reference-based control with time delay estimation (TDE) was introduced to compensate for unknown terms that are lumped into generalized disturbance and, consequently, guaranteed that the behavior of the system follows the output of the reference model. Nevertheless, the first-order derivative of the inductor current, which is difficult to accurately compute, was required. Furthermore, some nonlinear control techniques [28; 29; 30] have been adopted for DC-DC boost converters to increase the robustness of the voltage regulation. It should be noted that the above single loop structures possess cost-effectiveness, simplicity, and simple implementation; however, such regulation mechanisms cannot achieve the desired control performance. By virtue of exact voltage regulation for DC-DC step-up converters, the cascade control structure has been broadly adopted in numerous studies [31; 32; 33; 34] recently. For example, in [32], a linearized small-signal model around the operating point of a general N-phase interleaved boost converter was introduced, and a cascade control scheme with PID controllers using nominal parameters was subsequently established. The results showed that the proposed control approach was robust against parameter variations, and high conversion efficiency was also attained. Nevertheless, the performance of the closed-loop system varies with the distinct operation points. To overcome this drawback, a dual-loop control algorithm based on flatness control theory and active disturbance rejection control (ADRC) for two-phase interleaved boost converters (TIBCs) was introduced in [33; 34] where linear extended state observers (LESOs) were employed to estimate the uncertain input voltage and output current, and consequently, the output voltage was maintained at the desired level. In addition, disturbance observer-based control approaches [35; 36] were also investigated for stabilizing the output voltage of traditional DC-DC boost converters. Moreover, the integration of proportional-integral (PI) controllers used for the current loop and the ADRC for the outer loop has been a popular technique, which was employed in several existing works [19; 37] in robustly stabilizing the output voltage of floating IBCs (FIBCs) in recent years. In [13], [PERSON] et al. introduced a dual loop control scheme for a four-phase IBC, which has a backstepping-based current control law and STA-based voltage controller in the outer loop under the different working conditions in the presence of the deviations of circuit components. The control parameters were subsequently optimized by using the PSO algorithm. Furthermore, to increase the convergence rate of the inner current loop, the super-twisting algorithm (STA)-based controller was employed along with the ADRC developed for the outer voltage loop [17; 38]. However, it should be noted that the employment of the general super-twisting algorithm (GSTA) in developing the current controller and an ESO-based ADRC for regulating the output voltage of FIBCs has not been investigated in the literature. Motivated by the above analysis, in this paper, a nonlinear continuous ESO based on GSTA is introduced to cope with the lumped uncertainties in the system dynamics of the considered FIBC. In addition, the current controller is realized based on the GSTA, which ensures the inductor current follows the current reference in finite time. Thanks to that, a new ESO-based control approach is developed to increase the robustness of the closed-loop control system in the presence of a wide range of input variations and load changes, which have not been reported in the literature. The main contributions of this research work are summarized as follows:  
1. The finite-time boundedness stability of the GSTA-based controller for uncertain nonlinear first-order systems and GSTA-based ESO is rigorously proven by employing the Lyapunov theory. 2.