Performance robustness of a class of systems with multilinearly correlated perturbations

For a family of shifted and rotated systems with multilmearly correlated perturbations, the strict positive realness of the entire family can be inferred from the same property of its vertex systems. The maximal H∞ norm of the shifted system family is achieved at vertex systems. Two well-known strong Kharitonov-like theorems on performance robustness of interval system family are direct consequences of the above results.