The H-infinity control problem with constant scaling is considered. This problem is known to reduce to a search for matrices satisfying linear matrix inequalities (LMIs) and an additional nonconvex constraint. Recently, globally convergent algorithms to solve this nonconvex feasibility problem have been proposed. A major factor that determines the computational complexity is the number of nonconvex constraints. This paper gives verifiable conditions on the plant under which the reduction of nonconvex constraints is possible. The conditions appear to be a strong requirement, but in fact, they are nautrally satisfied in certain problems.