FREQUENCY RESPONSES UNDER PARAMETRIC UNCERTAINTY

A technique is developed for constructing value sets of a frequency re sponse in the presence of uncertain, parameters; it is based on the ge neral theorem on the structure of the boundary of the image of a set u nder a nonlinear mapping and on the notion of the inner and outer boun daries. The theory is illustrated by a number of examples admitting a closed-form, description of the image of a cube under linear, linear f ractional, multilinear, and some other mappings. The results obtained have numerous applications in robust stability and control.