This study proposes the application of a Lyapunov-based Model Predictive Control (L-MPC) approach to a 9-level Crossover Switches Cell (CSC9) converter operating in grid connection mode. The proposed method utilizes the structure of the classical finite-control-set MPC (FCS-MPC) technique while integrating a cost function that requires no tuning. By deriving the cost function based on Lyapunov theory, the system stability is ensured. Notably, the suggested approach offers several advantages over traditional MPC controllers. Firstly, it eliminates the need for gain tuning, thereby simplifying the implementation process. Secondly, the proposed controller prioritizes stability as a key design aspect. The presented simulation results prove that the proposed controller effectively regulates the voltage of the DC capacitor around its desired value and feed a smooth sinusoidal current to the grid with low total harmonic distortion (THD) while operating at a unity power factor.@en