New vertex results in H∞ performance of interval plants and interval feedback systems

The worst-case H_∞ norm of an interval plant weighted by p(s)/s^l(s +α) where l is an integer, α is a real number, and p(s) is an arbitrary polynomial, is achieved at one of the Kharitonov plants. Similar results hold for weighted sensitivity and complementary sensitivity functions of interval feedback systems. In this case, the admissible weights are of the form s+β/s^l(s+α)