Abstract: Algorithms of constructing reduced-order H_∞ controllers in explicit form are only applied to singular H_∞ control case. In order to apply these algorithms to nonsingular case, the matrix A of a generalized plant was divided into two parts A ₀ and Δ A , then ( A ₀, B ₂, C ₁, D ₁₂) or ( A ₀, B ₁, C ₂, D ₂₁) had unstable invariant zeros. Those algorithms could be used to the changed system to get a solution ( X , Y ) that could be used to construct a reduced-order controller. Since one of three linear matrix inequalities of the initial generalized plant was changed by the change of the system matrix A , the solution ( X , Y ) must be used in the linear matrix inequality that was changed with the variation of A for the initial generalized plant to see whether it could still hold or not. If it was holden, the solution ( X , Y ) could be used to construct a reduced-order controller for the initial generalized plant. Effectiveness of the algorithm was shown by numerical examples.