A simple algorithm for robust stability test under structured and unstructured perturbations

Discusses the problem of robust stability of a class of multivariable systems with both structured (parametric) and unstructured norm bounded uncertainties. The author first gives a vertex-edge criterion of robust stability of the closed-loop system. Next the author introduces the concept of the maximal difference of the phases of extreme points θ_m, by which the robust stability (or stability margin) of the multivariable system can be determined exactly. Finally, a simple algorithm for calculating θ_m is presented.