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The robust stability analysis of constrained model predictive control (CMPC) for linear time invariant and open-loop stable processes is the main topic of this paper. For the CMPC algorithm, the feedback controller is a piecewise linear operator due to the constraints. This piecewise linear operator can be thought of as an array of linear feedback controllers in parallel, handling different types of predicted active constraint situations. Each term in the linear operator corresponding to the predicted active constraint situation can be decomposed to have an uncertainty block. Hence, the linear operator can be written as a linear closed-form with uncertainty blocks inside. In this way, the robust stability of CMPC can be analyzed and a computer aided off-line tuning technique for the stability of CMPC can be developed by solving a minimum maximum problem based on the stability analysis method. Some examples are given to show the feasibility of the analysis and tuning methods.