Linear time computation of feasible regions for robust compensators (Q2755396)

The paper describes an application of computational geometry in robust control of continuous-time scalar linear systems affected by interval parametric uncertainty, where robustness is ensured by frequency domain criteria. The whole development relies on a comprehensive and accurate study of the boundary of the value set of the system transfer function, seen as a Minkowski quotient set of two Kharitonov rectangles in the complex plane. It is most notably shown that, at a given frequency, this boundary can be computed with an algorithm whose complexity is a linear function of the plant order, hence avoiding computationally intensive parameter gridding. This is a long, notationally difficult paper unveiling interesting and mostly unknown connections between computational geometry and control theory.