Unified Approach to Robust Performance of a Class of Transfer Functions with Multilinearly Correlated Perturbations

In this paper, we study the envelope of the Nyquist plots generated by a family of stable transfer functions with multilinearly correlated perturbations and show that the outer Nyquist envelope is generated by the Nyquist plots of the vertices of this family. We then apply this result to calculating the maximal H∞-norm and verifying the strict positive-realness condition for uncertain transfer function families. Vertex results for robust performance analysis are established. We also study the collection of Popov plots of this transfer function family and show that a large portion of its outer boundary comes from the vertices of this family. This result is then applied to the interval transfer function family to obtain a strong Kharitonov-like theorem.