We study stability of Model Predictive Control (MPC) with a quadratic cost function for LTI systems with a discrete input alphabet. Since this kind of systems may present a steady-state error, the focus is on practical stability, i.e., ultimate boundedness of solutions. To derive sufficient conditions for practical stability and characterize the ultimately invariant set, we analyze the one-step horizon solution and adapt tools used for convex MPC formulations.
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Aguilera et al. (2013) studied this question.
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