Stability robustness of linear systems to real parametric perturbations

Linear time-invariant systems subject to real, parametric variations are considered. The problem of computing the half-sidelength 1/μ_∞ of the largest stability hypercube in the parameter space is formulated in a frequency-independent way. The frequency-dependent approach developed in μ analysis is impracticable, because μ_∞ is a discontinuous function of frequency. The authors derive an accurate upper bound for μ_∞, using block-diagonal scaling of the largest singular value of a real, frequency-independent matrix M. The optimal scaling is found using quasi-convex optimization. A numerical example illustrates the method