Normal Matrix Approximations and their Use in the Assessment of Stability in the Presence of Uncertainty

Normal matrix approximations are deployed in order to derive a new method for the assessment of the stability of linear multivariable feedback systems in the presence of additive perturbations. The method provides guidelines for the deslgn of real controllers which attain the condition of normality and thus minimise the error of approximation. An alternative approach to design prescribes the systematic adjustment of the numerical range of the appropriate transfer function matrix as the means of achieving multivariable gain/phase sharing.