A tutorial comparison of three multivariable stability margins

The authors compare the utilization of three multivariable stability margins for stability analysis of multivariable linear and nonlinear dynamical systems. The three margins considered are those developed by R.W. Bass (1956, 1983), J.C. Doyle (1982) and M.G. Safonov and are commonly represented by ρ, μ, and K_m, respectively. These margins provide the analyst with varying degrees of both perturbation classification and structure. The mathematical definitions of each margin are presented with the corresponding implications as to the nature and structure of the perturbation. The three margins are then compared via a simple second-order example with real structured uncertainty. Some fundamental conclusions are then drawn to provide a commentary on the tutorial results