Exponential stability of mixed constrained model predictive control

Under the stabilizability and the detectability assumptions on the linear plant, it is shown for both state and output feedback cases that the stable (marginal) linear plant subject to the input constraints is globally (semi-globally) and exponentially stabilized in the sense of Lyapunov by the mixed constrained model predictive control law. It is also demonstrated that, for the marginal and unstable plant cases, the domain of attraction is the set of all initial conditions for which the mixed constrained model predictive control law is defined throughout the trajectory