Convergence analysis of a parametric robust H₂ controller synthesis algorithm

This paper presents an iterative algorithm for solving the parametric robust H₂ controller synthesis problem and analyzes the convergence properties of the algorithm on several examples. It is difficult to make concrete statements about the behavior of the iterative algorithms, except that it is often conjectured that the cost in each step of the solution procedure is reduced, which implies that the algorithms should converge to a local minimum. Similar difficulties exist for the new LMI-based iterative algorithm that we have recently proposed (1997) to solve the bilinear matrix inequalities that occur in robust H₂ control design. The effectiveness of the new algorithm has already been demonstrated on several numerical examples. This paper verifies that it efficiently converges to the optimal solution. In the process, we provide some new key insights on the proposed design technique which indicate that it exhibits properties similar to the D-K iteration of the complex μ/K_m-synthesis