## 1 Introduction  
Voltage source inverters (VSI) are among the most important power electronic circuits used in a variety of applications, including renewable energy systems, electric drives, and motor control. A VSI is a power electronic device that converts a DC voltage input into a variable-frequency and -amplitude AC output [1; 2; 3]. Voltage source inverters (buck inverters) generate an AC output instantaneous voltage always lower than their DC input [1; 2; 3]. When a larger voltage is required, a boost stage is required between the DC input and the buck inverter depending on the power level required; this option is a feasible solution, but the additional intermediate converter increases the cost and volume of the total system, as well as reduces the total efficiency. This is why the development of boost-type inverters is an active research field [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. One of the main topologies of boost-type inverters is the differential boost inverter, sometimes simply called the boost inverter, initially introduced in [4]. This converter gained significant attention from researchers in the following decades due to its ability to overcome the limitations of the conventional full-bridge inverter, which is well-established. Specifically, the DC-AC boost converter can generate AC voltages with amplitudes greater than the input DC voltage without requiring an additional conversion stage or increasing the number of power semiconductors. Figure 1a shows the discussed converter, which is made up of two identical cells that use symmetrical converters. The cells are connected back-to-back or in a bridge configuration, providing the output voltage differentially between their outputs. The converter can be divided into two single boost converters, each of them generating a  
DC-biased sinusoidal voltage; see the simplified diagram in Figure 1b. The DC bias is introduced since the boost converter cannot produce a voltage lower than its input. It is the same value for both converters, as the load is connected in a differential manner; this DC value is not reflected on the output. This can also be observed by applying [PERSON]'s voltage law (KVL) to the diagram of Figure 1b. From Figure 1b, it is also evident the DC bias must be the same in both converters to prevent a DC bias at the output voltage, which is expected to be an AC signal. Furthermore, sinusoidal signals generated by each boost converter must be shifted by 180\({}^{\circ}\). In this case, these amplitudes are added at the output side (see Figure 1c). One of the more interesting challenges in the boost converter is its control; it is a nonminimum phase system, which means that its linearized model has a right-half plane zero in the transfer function. Nevertheless, control can be performed, and it is widely used for regulation purposes. An example can be found in Appendix A. Another manner is to use an indirect method. Instead of directly controlling the capacitor's voltage, which makes the inductor current an unstable variable, the inductor current may be directly controlled with a reference chosen to obtain a certain capacitor's voltage (see Appendix B). Additionally, the boost inverter requires a trajectory tracking control which is more complex than the regulation-oriented control. These challenges require the use of advanced control techniques to achieve reliable and robust performance [10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. Among the different strategies of control applied to the boost inverter, the sliding mode control is one of the most investigated, and it has been widely recognized as an effective control strategy for power converters, including power boost converters. Sliding mode control has several advantages when applied to power boost converters, such as robustness to parameter variations and disturbances, fast transient response, and insensitivity to nonlinearities.