Representations of Real and Complex Stability Radii of 2-Dimensional Linear Systems

Rigorous proofs are given for the representations of real and complex stability radii of 2-dimensional linear systems. This representations can be used to analyze the robustness of a nominal 2-dimensional linear system under pelturbation of the system parameters, in particular testing the effect of numerical algorithms which are used to calculate the real stability radii of higher dimensional piecewise-linear systems.