Mixed Μ Problems and Branch and Bound Techniques

Abstract

The computation of the general structural singular value (μ) is NP hard, so quick solutions to medium sized problems must often be approximate. In many of the cases where the current approximate methods are unsatisfactory, improved solutions are highly desirable. It is shown that, despite their worst‐case combinatorial nature, branch and bound techniques can give substantially improved solutions with only moderate computational cost. © 1997 by John Wiley & Sons, Ltd.

Delay margin analysis of uncertain linear control systems using probabilistic µ

“…Fortunately, conservatism remains low in most cases, as highlighted in [14]. Moreover, [31] shows that it tends to zero when the size of D tends to zero.…”

Delay Margin Analysis of Uncertain Linear Control Systems Using Probabilistic μ$$ \mu $$

“…Fortunately, conservatism remains low in most cases, as highlighted in [8]. Moreover, [34], shows that it tends to zero when the size of tends to zero.…”

Advanced probabilistic μ-analysis techniques for AOCS validation

“…A branch-and-bound (B&B) algorithm can be used to explore the whole uncertainty domain. The idea is to partition B δ into smaller boxes until each box has guaranteed stability or is sufficiently small to be neglected [14]. Taking the union of the boxes with guaranteed stability leads to an approximation D s ⊂ B δ of the exact stability domain.…”