This paper considers the H infinity-control problem with constant diagonal scaling related to the robust control synthesis for systems with structured time-varying uncertainties, The problem is not convex in general, and hence it is difficult to find a global solution. The purpose of this paper is to provide an algorithm to find a suboptimal solution with any specified small tolerance from the globally optimal solution for the optimization problem, The algorithm based on the triangle covering method is proposed. The computational complexity analysis shows that its worst case order is polynomial in the inverse of the tolerance and the size of an a priori given interval of scaling with a fixed number of uncertainty blocks.