Stability Robustness of Linear Systems to Real Parametric Perturbations

L. El Ghaoui and S. Boyd

Proceedings of the 29th IEEE Conference on Decision and Control, 3:1247-1248, December 1990.

We consider linear time-invariant systems subject to real, parametric variations. The problem of computing the half-sidelength 1/mu_infinity of the largest stability hypercube in the parameter space is formulated in a frequency-independent way. The frequency-dependent approach developed in mu analysis is impracticable, because mu is a discontinuous function of frequency. We derive an accurate upper bound for mu_infinity, 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.