On the robust stability analysis with real block structured uncertainties

Accurate calculation of structured singular value is the key to robust stability analysis and control synthesis of a feedback system. The most commonly used tool in practice is the MATLAB Robust Control Toolbox where some upper and lower bounds of the structured singular value are calculated. Unfortunately, because of the discontinuities of the structured singular value with pure real perturbations, there is usually a large gap between the upper and the lower bounds obtained using this MATLAB toolbox when the system is subject to real parametric uncertainties. Motivated from the exact stability radius formula for unstructured real perturbations, we propose a modification of the real stability radius formula so that it can be applied to computing the stability radius with real block structured perturbations. Numerical simulations show that the proposed method can provide useful bounds when there are nontrivial real block structured uncertainties.