Extracting worst case perturbations for robustness analysis of parameter-dependent LTI systems

In this paper, we deal with robust performance analysis problems of LTI systems depending on uncertain parameters. By following existing scaling-based approaches, we firstly derive computationally tractable parameter-independent LMI conditions to assess the robust performance, which are conservative in general. What makes the present approach novel is to take the dual of those LMIs so that we can conclude the exactness of the analysis results. More precisely, we clarify that if the computed dual solution satisfies a certain rank condition, then we can ensure that the robust performance is never attained. In particular, we can extract the worst case perturbation that violates the underlying performance. Thus we provide viable tests for the exactness verification of LMI-based robust performance analysis.