## 1 Introduction  
The DC-AC boost converter, boost inverter, differential boost inverter or dual boost inverter, as it has been called by different authors in the literature, was introduced by [PERSON] and [PERSON] in the 1990s [1]. The potential that allowed this converter to attract the interest of researchers in the following decades was its ability to overcome the most restrictive limitations of the conventional and well-established full-bridge inverter. This is mainly related to the possibility of generating AC voltages with amplitudes larger than the input DC voltage without requiring more than one conversion stage or increasing the number of power semiconductors. This interesting topology is composed of two identical cells using symmetrical bidirectional boost DC-DC converters that share a back-to-back or bridge connection and differentially provide the output voltage between their outputs. This feature is characterized by a reduced common-mode noise but can be affected by DC current circulation in the load if the bias component of the output voltage of the cells is not correctly equalized [2]. Although the aforementioned features of the boost inverter are very attractive, these can only be achieved by developing more complex controllers or applying more complex methods to synthesize the required controllers. Compared with its counterpart, i.e., the full-bridge inverter, the highly nonlinear dynamic behavior of the output voltage as a function of the operating duty cycle makes devising an effective control solution difficult. The higher the required gain to generate the output voltage is, the higher is the effect of nonlinearity on the dynamic behavior causing that linear controllers cannot guarantee a proper operation. Further, we need to mention that the approach performance based on linear control is directly affected by the non-minimum phase nature of the output voltage to control the transfer function of each boost cell. Sliding-mode control (SMC) was practically the first approach in the reported literature applied to control a boost converter in the context of a stand-alone operation. In [1], [PERSON] and [PERSON] defined a sliding surface for each boost cell using a linear combination of current and voltage errors. Although the required voltage references were nothing more than two DC-biased sinusoidal waveforms with a 180\({}^{\circ}\) phase shift between them, the current references were difficult to synthesize because it depended on the input voltage and load current. Hence, the current-error component of the surfaces was obtained by measuring the high-frequency component of the inductor currents by assuming perfect tracking of the references in the stationary state. This approach was implemented using hysteresis comparators that then generated a variable switching frequency. This first proposal could be classified into a set of double-surface SMC (DS-SMC) approaches. A second method that employed SMC was introduced by [PERSON] et al. in [3] in which the control of both boost cells were correlated by complementarily coupling the commutation of the switches in the boost cells. In that work, a unique sliding surface was defined that involved the difference between the inductor currents and the proportional and integral actions that both operated under an output-voltage error. This second proposal, which could be classified as a single-surface SMC, was implemented using a single hysteresis comparator and required one less measurement because the voltage of the capacitors were not separately controlled. Furthermore, in the selected sliding surface, identifying the form of the well-known indirect control applied to regulate the output voltage of DC-DC converters was possible using an outer proportional-integral (PI) controller and a current inner loop. More recently, [PERSON] et al.