Kharitonov-like theorems for robust performance of interval systems

The sensitivity function of a control system is an important concept in performance analysis, classical filter design as well as modern robust H^∞ control. For an interval system, we prove that the maximal H^∞ norm of its sensitivity function is achieved at twelve (out of sixteen) Kharitonov vertices. Similar Kharitonov-like results are established for the complementary sensitivity function and strict positive realness of interval systems. These results are useful in robust performance analysis and H_∞ control design for dynamic systems under parametric perturbations.