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. The multipliers may be used in a general and versatile analysis of the robust stability of input constrained model predictive control.
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Heath et al. (2007) studied this question.
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