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This paper discusses an on-line approach to Model Predictive Control (MPC) of input constrained linear systems. First, it is shown that an example of MPC with one-side input constraints is reduced into the Linear Complementarity (LC) Problem with M -matrix, which can be more efficiently solved by the existing special algorithm than the other general algorithms such as the Lemke method. However, in the case of both-side input constraints, which is more practical from the control engineeringdoi:10.1016/s1474-6670(17)31698-1 fatcat:46chh5mah5beri5u2py6j2ju4u