Computational Complexity Analysis for Constantly Scaled H_∞ Control Global Optimization Problem

Block-Diagonal Case

Abstract

The H_∞ control problem with block-diagonal 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 sub-optimal solution with any specified small tolerance from the globally optimal solution for the optimization problem. We analyze the computational complexity of the algorithm and show that its worst case order is polynomial in the inverse of the tolerance, with fixed size of scaling matrix.