Extension of the Nyquist robust stability margin to systems with nonconvex value sets

The Nyquist robust stability margin is proposed as a measure of robust stability for systems with affine parametric uncertainty. The work extends the critical-direction theory to include nonconvex critical uncertainty value sets through the introduction of a more general definition of the critical perturbation radius. The approach is specialized to the case of real parametric affine uncertainty models, and it is shown that the critical perturbation radius can be calculated precisely using an explicit map from the parameter space to the Nyquist plane