Elliptical bounds, robustness, and performance in control system design

Generalizations of the standard singular-value robust stability and nominal performance criteria are proven. The robustness test allows the inclusion of information about the structure of uncertainty, and the nominal performance result allows independent constraints on each input channel. These tests provide a natural characterization of sensitivity and complementary sensitivity weighting matrices for sensitivity minimization problems. An H^∞ optimization problem is presented which provides a method of synthesizing controllers satisfying these requirements based on the solution of the general distance problem.