An iterative approach to the robust H∞ synthesis problem with a sequence of infeasible controllers

This paper aims to design a robust H_∞ control system against time invariant polytopic uncertainties. In general, such robust control problems are described by parameter dependent bilinear matrix inequality (PDBMI) problems which are not tractable numerically and there are few efficient methods for solving them. In this paper, we propose an iterative approach to the robust H_∞ controller synthesis problems, which constructs a sequence of infeasible controllers. The feature of our approach is to be able to use any controller variables which may not be a robust stabilizing controller as an initial point. The efficiency of our approach is shown by a numerical example.