Robust performance with respect to diagonal input uncertainty

The robust performance problem of keeping the output sensitivity function small despite the presence of block diagonal uncertainty at the plant input is studied using sensitivity analysis as well as structured singular value analysis. It is shown that the robust performance is primarily determined by the first- and second-order effects of input uncertainty on the output sensitivity function. Robustness indicators are derived as functions of both the plant condition number and its input directionality properties. These indicators are useful in detecting potential design difficulties associated with ill-conditioned plants when input uncertainty is block diagonal, and they appear to give more accurate information than the plant relative gain array