Methods to check robust stability in the parameter space

In the analysis and design of robust control systems, it is essential to check whether the closed-loop system is stable or not in a given perturbation area of the parameter space. Two methods for checking the robust stability in a perturbation domain of interest are considered. The first is the classical positivity checking approach based on the Routh-Hurwitz theorem and minima search, and the second is the polytopic polynomial approach with a dynamic perturbation domain dividing technique. Both approaches can be employed to compute the real-structured singular value or the real multivariable stability margin and to locate all unstable regions in a given perturbation domain.<>