The exact calculation of real stability radii of systems with affine parametric uncertainties

By transforming the affine parametric uncertain system problem into a linear feasibility problem, a new and simple approach to the problem of finding robust stability margins for SISO systems with real affine parametric uncertainties is proposed. The approach recovers previous results using real-p analysis given in the literature. A comprehensive example shows that these approaches are equivalent in solving for the parametric stability margin for the affine uncertainty problem. The results in this paper demonstrate that the stability radius approach may be promising in solving more general real structured uncertainty problems with general value-sets.