A sufficient condition for the stability of optimizing controllers with saturating actuators

The quadratic programme that must be solved with certain output–feedback model predictive controllers can be expressed as a continuous sector‐bounded nonlinearity together with two linear transformations. Thus, the multivariable circle criterion gives a simple test for stability, with or without model mismatch. In particular, it may be applied if the open‐loop plant is stable and the actuators are subject to simple saturation constraints. In the case of single horizon model predictive control, it suffices to check for positive realness a transfer function matrix whose dimension corresponds to the number of inputs. For an arbitrary length receding horizon it suffices to check the poles of a low dimension transfer function matrix and the eigenvalues (over an appropriate range of operator values) of a matrix whose dimension is independent of the horizon length. Copyright © 2005 John Wiley & Sons, Ltd.