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This paper studies Tube Model Predictive Control (MPC) with a Sliding Mode Controller (SMC) as an auxiliary controller. It is shown how to calculate the tube widths under SMC control, and thus how much the constraints of the nominal MPC have to be tightened in order to achieve robust stability and constraint fulfillment.  The analysis avoids the assumption of infinitely fast switching in the SMC controller

Tube Model Predictive Control with an Auxiliary Sliding Mode Controller