In the recent years, the introduction of an alternative energy such as clean energy has become a major challenge. In this context, several sources of energy are often associated to provide the required energy to the grid. However, output of photovoltaic system and wind turbine is influenced by meteorological conditions. As a result, the power quality exchanged between those sources and the grid might be affected. In this paper, we suggest a new structure of hybrid multi-level inverter in order to solve problems due to the rapid variation of exchanged powers. The main objective of the proposed structure is to limit the sudden fluctuation of injected power into the electrical network via a new structure of multi-level inverter based on intermediate supercapacitor energy storage. The control strategy of this hybrid inverter applies linear matrix inequalities technique to control the injected or absorbed currents by the storage system as well as space vector modulation technique to generate pulses for switches. Presented results highlight the efficiency of the proposed system in suppressing short-term power fluctuations.