Performance robustness of a class of systems with multilinearly correlated perturbations
The robustness study of interval systems or linearly perturbed systems is nearing maturity, whereas the robustness study of multilinearly or nonlinearly perturbed systems is still in its infancy. For a family of shifted and rotated systems with multilinearly correlated perturbations the strict positive realness of the entire family can be inferred from the same property of its vertex systems. The main results of the paper show that the maximal \(H^\infty\) norm of a family of shifted systems with multilinearly correlated perturbations is obtained at its vertex systems. Thus, the robustness issues of strict positive realness and \(H^\infty\) norm are unified in one theoretical framework. Two well-known strong sixteen-vertex-verification Kharitonov-like theorems on performance robustness of an interval system family are direct consequences of the above results. The results presented in the paper are also suitable for the robust absolute stability analysis of uncertain systems. The paper is mathematically dense. The references are somewhat antiquated.
scientific article; zbMATH DE number 850851