The paper deals with the two-block \(H^\infty\) control problem for linear distributed parameter plants with finitely many unstable modes. Under the assumption that the weighting filters in the \(H^\infty\) mixed-sensitivity problem are finite-dimensional, the authors develop a unified approach for solving both the optimal and the suboptimal problem. They obtain two systems of linear equations, expressed in terms of state-space realizations of the finite-dimensional parts of the problem data as opposed to the values of certain analytical functions at the roots of certain polynomials, as some earlier papers had done. This alternative approach alleviates or totally eliminates numerical ill-conditioning associated with the earlier approach in the computation of \(H^\infty\) optimal and suboptimal controllers.