Sensitivity and Complementary Sensitivity Integrals Applied to a Class of Ill-Conditioned Plants

We consider a standard robust performance problem for two input, two output diagonal systems. By using the classical sensitivity integral together with an analogous result for the complementary sensitivity function, we derive an upper bound that the plant condition number must satisfy if robust performance is to be achievable. The upper bound is given in terms of the weighting functions used to represent the design specifications.