This paper presents a coordinated control strategy based on direct Lyapunov theory to handle the consistency of AC grids in a multi-terminal (MT) modular multilevel converter (MMC)-HVDC systems during varying both loads and DC link voltage. As the first contribution, a set of dynamic equations is proposed based on separating the dynamics of MMCs upper and lower arms state variables. The dynamics consists of only their related upper/lower arms state variables leading to more effective components for the steady state terms of proposed control technique. To develop the dynamic parts of the controller, the global asymptotical stability of MT MMC-HVDC system is assessed by direct Lyapunov method. As another advantage of the separated dynamic equations, the Lyapunov theory is able to exploit very simple decoupled components for the dynamic parts of proposed control functions. Moreover, in order to specify the variation trend of Lyapunov coefficients, further stability analysis contributes to demonstrating the effects of Lyapunov coefficients on the MMCs state variable errors and its dynamic. As another main contribution of this paper, two independent capability curves based on the power injection capability of the MMCs upper and lower arms, are obtained which will be assessed through changing the input and output voltages as well as MMC parameters. Finally, simulation results in MATLAB software are utilized to verify the validity of proposed control strategy.