The quadratic programme that must be solved with certain
output-feedback model predictive controllers can be expressed as a
continuous sector-bounded non-linearity together with two linear
transformations. Thus the multivariable circle criterion gives a
simple test for robust stability. 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.