Some Extensions of the Gain Margin Maximization Problem for Uncertain Parameter Plants with Sensitivity Constraints

We consider robust stabilization and the weighted sensitivity or complementary sensitivity minimization for SISO plants with a real uncertain parameter which may occur either in the numerator or denominator of the plant transfer function. We derive necessary and sufficient conditions for the existence of robust controllers. Their structure and parameterization can be obtained from the corresponding Nevanlinna-Pick interpolation problems. This work extends the previously known case of an uncertain gain parameter and sensitivity minimization.