Conservatism with robustness tests for linear feedback control systems

This paper examines a variety of techniques for assessing stability robustness of linear multivariable feed-back control systems to model uncertainty in the open-loop plant, which is represented as an additive or multiplicative dynamic perturbation to the nominal plant transfer function matrix. It addresses the issue of conservation with certain robustness tests based on matrix norms and measures by exploiting known relationships between those quantities and the eigenvalues of a matrix. Techniques for selecting transformations to reduce conservatism for several classes of uncertainty are identified. Relative conservatism of various robustness tests is illustrated for a two-input/two-output example.