K-s-φ Iteration for Robust H2 Controller Synthesis

An iterative procedure is proposed for robust H2 controller design. This method improves a previously reported technique, where optimization over two variables the controller and a scaling matrix was carried out by keeping one fixed at a time and minimizing the worst-case H2 norm over the other. In this paper, it is shown how optimization over both parameters at the same time can be formulated as an LMI problem with an additional constraint. Application to a well-known benchmark problem illustrates that this approach leads to a significantly larger range of feasible solutions, thus allowing the synthesis of controllers that guarantee robust performance over a larger range of uncertain parameters.