Parametric robust H∞ controller synthesis: comparison and convergence analysis

Our previous papers (1996, 1997) have demonstrated the effectiveness of our iterative algorithm using linear matrix inequalities (LMIs) on several parametric robust H_∞ control designs. This paper presents two additional important components to the discussion on the behavior of the new LMI-based iterative algorithm: a comparison study between the LMI synthesis technique and the existing iterative approaches of the complex and mixed μ/K_m synthesis; and a convergence analysis of this new algorithm. The results indicate that the Popov H_∞ controller synthesis provides a viable alternative for designing real parametric robust controllers and exhibits properties similar to the D-K and D,G-K iteration of the complex and mixed μ/K_m synthesis. The key potential advantage of using the LMI approach is the elimination of the curve-fitting for the D and G scaling functions