## 1 Introduction
A rule-based cascade controller that determined a component to be added to the voltage references in order to cancel the second-order harmonic of the input current was developed in [10]. The proposed scheme required the measurement of the ripple component of the input current to compute the amplitude and phase of the voltage references of the cascade loops that included a voltage outer loop and a current inner loop per boost cell. The innovative feature of this controller was the use of a perturb and observe algorithm that computed the amplitude and phase of the required additional components. Again, a similar cascade-control scheme was proposed in [11] where an additional outer loop generated the added components from the measurement of the AC component of the input current. The proposed loop separately determined the AC components to avoid undesired phase shifts. The common feature of these last three controllers was the use of harmonic-enriched references in the capacitor-voltage control loops, which increased the ability of the control system to perform a second function in addition to the tracking of the output voltage or current. Other interesting works that improved the control of boost inverters can be found into battery-charging [12; 13] and fuel-cell-based applications [14; 15]. This study presents an alternative DS-SMC approach that is applied to a boost inverter in which the boost cells are independently commutated using one cascade controller per cell, thereby enforcing tracking of harmonic-enriched reference waveforms to shape the capacitor voltage. Second- and fourth-order terms are introduced to reduce the instantaneous-voltage gain of the cells, which results in the alleviation of the voltage stress of the switches throughout the period of the output voltage, as previously assessed in [16] where the same converter was modified by introducing additional power semiconductors and using half-cycle rectified voltage references. In contrast to the SMC approach developed in [4], the proposed control requires two additional voltage measurements, one additional hysteresis comparator and a complementary reference generator to produce the two required harmonic components. Although this last aspect supposes an increment in terms of cost of the solution, the three required voltage measurements share the same electric reference which suppose no need of isolation. Furthermore, since isolation is preferred for increased values of nominal power of the inverter, the cost of the additional electronics will become irrelevant. Beside this, complexity of the system is not really affected because the control philosophy is the same (hysteresis comparison and PI outer loop). The size of the electronic circuit or the computational cost increase depending on the type of implementation, but this aspect is not comparable with the considerable reduction of the semiconductor voltage stress. The rest of the study is organized as follows: The boost converter operation and the fundamentals of the performance improvement are presented in Section 2. After that, in Section 3, the ideal sliding motion is analyzed for the entire range of operation conditions using the harmonic balance technique. The constraints to ensure asymptotic stability when tracking the required periodic behavior are provided as well as a simplified model of the inner loop dynamics. The fundamentals for synthesis and implementation of the outer controllers are also explained. Comparative simulation results demonstrate the feasibility and advantages of the proposed control in Section 4. Finally, conclusions and future work are presented in Section 5.