Robust stability analysis of constrained l1‐norm model predictive control

Abstract Sufficient conditions for robust closed‐loop stability of a class of dynamic matrix control (DMC) systems are presented. The l 1 ‐norm is used in the objective function of the on‐line optimization, thus resulting in a linear programming problem. The ideas of this work, however, are expandable to other DMC‐type controllers. The keys to the stability conditions are: to use an end‐condition in the moving horizon on‐line optimization; to have coefficients of the move suppression term in the objective function of the on‐line optimization satisfy certain inequalities; and to express the uncertainty as deviations in the unit pulse response coefficients of the nominal plant. These deviations and disturbances must also satisfy certain inequalities. An off‐line tuning procedure for robust stability and performance of a class of DMC controllers is also included, which determines an optimal moving horizon length and optimal values for coefficients of the move suppression term. The applicability of our approach is elucidated through numerical simulations.