Advanced computation of the robustness margin

When applying /spl mu/ analysis, the use of a frequency gridding may reveal unreliable in the specific context of narrow and high peaks on the /spl mu/ plot (typically in the case of uncertain lightly damped systems). A solution for avoiding this gridding is to transform the problem into an augmented /spl mu/ problem, in which the frequency is treated as an additional uncertainty. Two problems are considered: 1) the direct computation of the maximal structured singular value over an interval [/spl omega/_,/spl omega/~] (direct approach); and 2) given a frequency /spl omega/_ and a level K of uncertainty, compute the maximal value of /spl omega/~, such that the robustness margin inside [/spl omega/_, /spl omega/~] is greater than K (dual approach). A skewed /spl mu/ problem is obtained, in which the frequency is treated as a one-sided uncertainty. A generalized /spl mu/ upper bound is proposed as a solution to this problem. Finally, we illustrate on a classical example that an efficient solution for computing the robustness margin combines the direct and dual approaches with a frequency gridding.