Design problems for sensitivity and complementary sensitivity

Two design problems involving sensitivity and complementary sensitivity are examined in this paper. First, we characterize all pairs of constraints on the sensitivity and the complementary sensitivity which can be simultaneously satisfied in a closed-loop system for a given scalar plant in the context of time-invariant control. Second, we present a simple one-to-one correspondence between solutions of the sensitivity problem and of the complementary sensitivity problem for a multivariable plant.