STABILITY ROBUSTNESS MARGIN COMPUTATION FOR STRUCTURED REAL-PARAMETER PERTURBATIONS

An efficient computational method is presented for stability robustness analysis with structured real-parameter perturbations. A generic model of a class of uncertain dynamical systems is used as an example. The parameter uncertainty is characterized by a real scalar perturbation variable. Multilinearity of the closed-loop characteristic polynominal is exploited to permit application of the mapping theorem to calculate the stability robustness margin. It is found that the stability boundary of the perturbation variable exhibits sensitive geometry in the frequency domain, which renders problematic the task of minimizing this variable as a function of frequency. This difficulty is avoided by calculating the minimum distance to the image of the uncertainty domain over frequency as a function of the perturbation. It is also shown that a certain class of uncertain dynamical systems has the required multilinearity property and is thus amenable to the proposed technique.