Computing the frequency response of systems affinely depending on uncertain parameters

The computation of the frequency response of systems depending affinely on uncertain parameters can be reduced to that of all its one-dimensional edge plants while the image of such an edge plant at a fixed frequency is an arc or a line segment in the complex plane. Based on this conclusion, four computational formulas of the maximal and minimal (maxi-mini) magnitudes and phases of an edge plant at a fixed frequency are given. The formulas, besides sharing a simpler form of expression, concretely display how the extrema of the frequency response of the edge plant relate to the typical characteristics of the arc and line segment such as the centre, radius and tangent points of the arc, the distance from the origin to the line segment etc. The direct application of the results is to compute the Bode-, Nichols- and Nyquist-plot collections of the systems which are needed in robustness analysis and design