In this paper, we are considering the problem of controlling a single-phase 3-celles inverter with LC output filter connected photovoltaic systems. The control objectives are: i) achievement of the maximum power point tracking (MPPT) for the PV array ii) ensuring a good convergence of the voltages across the flying capacitors iii) generating a perfectly sinusoidal voltage to the inverter output with amplitude and frequency fixed by the reference signal. The controller is designed using the backstepping approach in its adaptive versions and the Lyapunov stability argument. The whole system is described by 6th order nonlinear mathematical model and controlled by using the backstepping approach and tools from Lyapunov stability. To demonstrate the performance of methods, some results of the overall system simulations are presented under MATLAB/Simulink software.