Real Structured Singular Value Synthesis Using the Scaled Popov Criterion

The scaled Popov criterion is used to derive an upper bound for the worst-case HI norm over a set of linear, time-invariant, norm-bounded, block-structured parameter perturbations. This upper bound provides the basis for a robust controller synthesis procedure that minimizes the upper bound and guarantees asymptotic stability of the closed-loop system for all real parameter perturbations in the specified set. Numerical examples demonstrate the tradeoff between achievable H2 performance and guaranteed robustness to real parameter perturbations as well as the reduction in conservatism due to the scaling matrix. Controllers designed for flexible structures using this technique are shown to have similarities to maximum entropy controllers designed for the same examples.