## 1 Introduction
have reemployed the same technique by preserving the coupled control action between the converter cells and applying an equivalent control technique to provide an analytical solution for synthesizing the outer voltage controller [4]. From the perspective of that work, the converter was controlled by imposing a periodic reference to the difference between the input currents of the cells, which in turn was generated by a PI outer loop that was configured to enforce the desired shape on the output voltage. That work also employs a hysteresis comparator for implementation. Finally, from a different perspective of the SMC application in this field and using a constant-frequency modulator, [PERSON] et al. developed an adaptive fuzzy-neural-network control (AFNNC) in combination with a total sliding-mode controller [5]. To design the controller, an additional loop, called as curbing controller, allowed modification of the sliding surface to cope with unpredictable disturbances, whereas the AFNNC modified the sliding-surface parameters to ensure permanent stability. Naturally, despite the achieved good performance, the required implementation was considerably complex compared with that in [4]. In addition, SMC has been applied to the control of boost inverters in grid-connected applications, which is similar to the work reported in [6] in which a boost-inverter-based hybrid energy-storage system (HESS) integrates both batteries and supercapacitors to the grid using two sliding-mode controllers. A particular aspect to consider regarding this work is the fact that the system can be considered as two boost inverters that share the connection to the cell capacitors and then share the AC-side differential connection. The complexity of the control in this approach then comes from the power control used to inject apparent power into the grid (both active and reactive power), the control used to impose the charge-discharge regimes of the storage devices and the compact configuration of the HESS. More recently, following the interest in systems involving batteries and fuel cells, researchers have paid more attention to the input-current behavior of the boost inverter mainly because of the scientific results that demonstrate that the ripple content exerts an important negative effect on the lifetime of storage devices. In a stand-alone case, to adequately shape the output voltage, the control must minimize the ripple content of the input current, which constitutes an important control objective. As expected, the simultaneous accomplishment of these two functions results in new stationary behavior in the inner variables, which is reflected in their harmonic content. In [7], [PERSON] et al. presented a cascade-control approach based on the use of a linearization function that evolved depending on the load and input-voltage operating conditions. A particular feature of this proposal was the use of three voltage measurements that shared the same reference and that no current measurement was required. Similarly, [PERSON] el al. proposed in [8] a waveform control using a cascade controller with two loops: one that shaped the voltage of the capacitors of the boost cells and the other that shaped the overall output voltage. These two controllers exhibited the characteristic of avoiding the use of current measurements. In the grid-connected case, the control of the inverter forces the shape of not only the output voltage, but also the current to inject the generated power into the grid. This application of the boost inverter was explored by [PERSON] and [PERSON] et al. in [9] using a cascade-control scheme that involved a loop compensation of the nonlinear gain of each boost cell and then provided the reference of the inner loops that affected the inductor currents. Similar to the stand-alone case, the enforcement of the input current to be simultaneously constant with the primary control objective implies an adjustment of the stationary behavior of the converter variables.