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SUMMARYThe 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.

Abstract-A novel approach is presented to accurately measure the scattering parameters as well as the radiation pattern of planar antennas that operate in the millimeter-wave frequency band. To avoid interconnection problems, RF probes have been used to connect to the antenna. These RF probes are normally used for the characterisation of devices on a semiconductor wafer. Here, they are used to characterise antennas that can be realised in any planar manufacturing technology. A completely planar transition is designed to transform the coplanar waveguide transmission line that is required by the RF probe to a microstrip line. It is shown that this transition can be de-embedded from the measurements. Moreover, a measurement setup has been built for the measurement of the far-field radiation pattern of millimeterwave antennas and antenna arrays. This setup allows to connect the antenna under test with an RF probe and can measure the radiation pattern in the whole upper hemisphere.

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