Global optimization for ℋ∞ control with block-diagonal constant scaling

The ℋ_∞ control problem with constant scaling is considered. 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 global solution with any specified tolerance for the optimization problem. We introduce the k-submatrix solvability test algorithm in order to develop a desirable algorithm. It is shown that we can obtain a 1-submatrix solvability test algorithm and that it is possible to find a global solution by combining a branch and bound type algorithm. We also analyze its computational complexity and show that the worst case computational complexity is of polynomial order in the inverse of the tolerance