ρ-synthesis: a `rhobustness´ margin for unstructured nonlinear and time-varying deviations

The author previously (1956, 1983) presented a robustness margin (which is available as a public domain MATLAB add-on toolkit). Although in some cases this criterion is identical to a criterion introduced independently by J.C. Doyle (1982) and by M.G. Safonov (1982), it is shown that in general the author´s criterion produces LOG-type control system designs which are more conservative in the anticipated bounds on permissible uncertainties (in the unstructured, norm bounded perturbation case). Nevertheless, it is advocated that ρ-syntheses should be performed simultaneously with μ-syntheses in order to illustrate the range of options available. For certain applications, the much lower bandwidth requirements of ρ-synthesis may outweigh the greater robustness (or passive adaptivity) of μ-synthesis. Also, there are more technical advantages, such as invariance of the overshoot factor, and only marginal variance of the rate of exponential asymptotic stability and response to external disturbances