Frequency response of uncertain systems with interval plants

This note provides simplification results concerning frequency domain properties of systems containing an interval plant. The problem is formulated in a general enough manner to encompass most problems involving one interval plant. It is shown that under rather mild assumptions, all the key information can be obtained using just 32 one-dimensional subsets of the interval plant called the 32 segments. For the general problem, it is not possible to avoid dealing with the segments. However, for the special yet important case of computing open-loop Bode plots, this note shows that eight subpolynomials of the interval plant are sufficient.