  Conditions for input-output stability of barrier-based model predictive
control of linear systems with linear and convex nonlinear (hard or soft)
constraints are established through the construction of integral quadratic
constraints (IQCs). The IQCs can be used to establish sufficient conditions for
global closed-loop stability. In particular conditions for robust stability can
be obtained in the presence of unstructured model uncertainty. IQCs with both
static and dynamic multipliers are developed and appropriate convex searches
for the multipliers are presented. The effectiveness of the robust stability
analysis is demonstrated with an illustrative numerical example.
