Abstract
This paper considers the H∞ control problem with constant diagonal scaling related to the robust control synthesis for systems with structured time-varying uncertainties. It has not been found that the general output feedback problem can be reduced to a convex optimization problem, and hence only a locally optimal solution can be obtained instead of the global one. The purpose of this paper is to provide an algorithm to find a suboptimal solution with any specified small tolerance or a globally optimal solution for the constantly scaled H∞ control problem. We introduce notions of ∈-feasibility and ∈-feasibility test algorithm in order to develop desired algorithms. It is shown that we can get an algorithm to find a sub-optimal solution within tolerance ∈>0 by combining the bisection method, if we have an ∈-feasibility test algorithm. The ∈-feasibility test algorithm named rectangle covering method is proposed. We also show that the worst case computational complexity is of polynomial order in the inverse of tolerance and the size of a priori given interval of scaling.
