In this thesis, we consider “exact” and “approximate” versions of the disturbance decoupling problem and the noninteracting control problem for linear, time-invariant systems. In the exact versions of these problems, we obtain necessary and sufficient conditions for the existence of an internally stabilizing dynamic output feedback controller such that prespecified interactions between certain sets of inputs and certain sets of outputs are annihilated in the closed-loop system. In the approximate version of these problems we require these interactions to be quenched in the ‘Hoo sense, up to any degree of accuracy. The solvability of the noninteracting control problems are shown to be equivalent to the existence of a common solution to two linear matrix equations over a principal ideal domain. A common solution to these equations exists if and only if the equations each have a solution and a bilateral matrix equation is solvable. This yields a system theoretical interpretation for the solvability of the original noninteracting control problem.