In constrained linear model predictive control a quadratic program must be solved on-
line at each control step, and this constitutes a nonlinearity. If zero is a feasible point for
this quadratic program then the resultant nonlinearity is sector bounded. We show that if
the nonlinearity is static then it is also monotone and slope restricted; hence we show the
existence of Zames-Falb multipliers for such a nonlinearity. We express the results in
terms of integral quadratic constraints. The multipliers may be used in a general and
versatile analysis of the robust stability of input constrained model predictive control.