Mixed-μ-Analysis for Flexible Systems. Part I: Theory

摘要

This paper presents new tools for computing upper and lower bounds of μ without frequency gridding. The proposed techniques for computing lower bounds of the peaks of the μ-curve, are divided into two steps. The first one consists of finding the perturbation with minimum Frobenius norm that leads to the limit of stability. Using this result as an initialization, the second algorithm finds the perturbation with minimum sigma-max norm such that the system remains at the limit of stability. Thelimit of stability is considered both from a state space and from a transfer matrix point of view, which leads to two classes of techniques. The lower bounds are validated by using an upper-bound analysis technique that considers standard scalings over arange of frequencies instead of at an isolated frequency.