A dilated LMI approach to robust H∞ static state feedback controller synthesis

This paper introduces a dilated Linear Matrix Inequality (LMI) approach to the robust H_∞ analysis for linear continuous-time uncertain systems. This approach has the interesting property that it provides LMI conditions in which the state matrix is separated from the Lyapunov variable. In addition, it is also shown, in this paper, that the obtained dilated LMI conditions always encompass the quadratic ones. Altogether, these facts will guarantee that the provided solutions will be, at worst, as good as the ones obtained by the quadratic approach. These results are shown to also hold for the robust H_∞ state-feedback control synthesis problem. A numerical example is presented to illustrate the advantages of the proposed method.