Guaranteed roll-off in a class of high-gain feedback design problems

A number of synthesis problems associated with (almost) disturbance decoupling by state or measurement feedback is considered. Starting from a mathematical definition of the notion of high-frequency roll-off, known results on the solvability of these problems are generalized to the situation in which we require their solvability together with a certain guaranteed roll-off between disturbance and control. The conditions are formulated in terms of the solvability and approximate solvability of certain matrix equations in rational functions.