Based upon the PWA model of the closed-loop MPC system and upon the tools developed for analysis of hybrid systems, convergence analysis of the closed loop MPC system are studied. Convergence analysis of predictive control system consists of stability analysis and feasibility analysis of MPC system. By trying to find piece wise quadratic Lyapunov function over the state's regions, which is cast as a LMI problem, the stability of closed-loop MPC system is analyzed. The feasibility of the closed loop MPC system is analyzed by calculating the maximal control invariant set of MPC system. At the end of the paper, simulations for a vibration control of elevator's mechanical system are made.