## 1 Introduction
In [29; 30], other control techniques have also been applied on a similar framework but the unpredictable nature of RESs is not taken into consideration. Various linear control schemes, aiming to achieve the voltage stability at DC bus, have been proposed in [20; 31; 32], however, suggested methods mostly discard the non-linear features of DC-DC converters, and control exertion will restrict to a smaller region. Ref. [19] suggests a robust \(H_{\infty}\) controller to address the restraints by assuming the uncertainties at the load; however, stability analysis is not ensured rigorously. The droop control method is frequently applied for DC bus voltage regulation, and [33] proposed the adaptive droop control, but communication delay occurs when multiple sources, such as wind system, PV system, and ESSs, are connected. In [34], an interlinked AC and DC subgrid model is proposed to implement the coordinate controller. However, the proposed model does not consider the intermittency of RESs in the structure. Moreover, it results in voltage fluctuation in the presence of multiple energy sources. Some additional linear control methods are proposed in [16; 33; 35; 36], but the behavior of RESs with power converters and ESS is not modeled. The literature discussed so far shows that substantial work has been performed to ensure the stability of DC and AC bus voltage of the microgrid. Typically, linear control methods were presented. However, the uncertain behavior of RESs exhibits dynamic operating regions for microgrid's operation. Therefore, performance inadequacy occurs for linear controllers to mitigate the fast transients, e.g., sudden cut-off at generation end, the quick change in load, etc. Some non-linear control methods for hybrid AC/DC microgrids are presented in [18; 28; 37]. In [18], the proposed hybrid AC/DC microgrid offers integral terminal sliding mode control for the machine side and grid side for on-grid and off-grid mode. The stable voltage at the AC and DC bus is achieved under different weather conditions but due to the presence of hybrid RES and hybrid ESS, the intricacy of the system increases. Ref. [18] offers an integral back-stepping based non-linear control which ensures the regulation of the DC bus. However, the proposed model only operates in islanding mode. Moreover, two control techniques are integrated which causes involvedness. Ref. [38] presents a hybrid AC/DC microgrid directly connected with the grid without considering any ESS in the system. A non-linear sliding mode controller has been proposed in [21; 39] to achieve DC bus voltage regulation, but the controller has limitations as it shows chattering and less profound to external disturbances. A recent study, Ref. [40], provides a double integral sliding mode controller to address the chattering and external disturbances issues. However, this study only considers the DC microgrid with a hybrid energy storage system and ensures energy management and tight DC bus voltage regulation. In [41], an adaptive Lyapunov redesign approach is suggested for power converters associated with renewable sources and hybrid energy storage systems considering the model uncertainties in the system. It guarantees the DC voltage regulation and energy management in the system but does not consider any DC-AC inverter in the system. In [42], Lyapunov-based non-linear control for RESs has been proposed where it provides the secondary support to AC subgrid during the on-grid mode by ensuring frequency, voltage, and power system stabilization. Keeping in view all the problems mentioned above, it is evident that hybrid AC/DC microgrid having different distributed generators, energy storage elements, and AC/DC loads are always challenging work. The unpredicted behavior of RESs under changing weather conditions drastically affects the stability of the grid [18]. Moreover, the constant power loads (CPL) at the DC side of the grid degrades the performance of the system [42].