Application issues in μ analysis

The real-μ analysis method determines the largest variations that guarantee closed-loop stability for a specified set of parameters. The specific focus of this paper is the effect of the relative scaling of the parameter uncertainties on the allowable uncertainty region for guaranteed stability (e.g. given a fixed set of uncertain real parameters, how does the choice of the scaling on each uncertainty affect the size of the hypercube for which stability is guaranteed.) This is important because it determines the sensitivity of the system stability to individual parameter changes in the presence of simultaneous variations. It is shown that system sensitivity to parameter variation is different if considering single perturbations in a set of simultaneous variations versus single parameter variations to a nominal model. Also, the “best” choice of relative scaling which provides the largest robustness margin for a given set of uncertain parameters is sought