This paper presents a new algorithm for designing full order LTI controllers for systems with real parametric uncertainty. The approach is based on the robust L2 gain analysis of the Lur'e system using Popov analysis and multipliers. The core algorithm, previously applied to the robust H2 performance synthesis problem, is shown to be applicable to the robust controller design with the H1 cost. Although the performance metrics are di erent, we demonstrate that the same solution algorithm based on LMI synthesis leads to a very effective and e cient technique for real parametric robust H1 control design. Furthermore, it is di cult to compare robust H2 controllers to =Km designs, but in this work we provide insights into the issue of conservatism for various robust H1 control approaches, in particular, the Popov controller synthesis, the robust H1 design, and the =Km synthesis. The detailed analysis of these approaches is demonstrated on a exible structure benchmark problem. Keywords: Lur'e system, real parametric uncertainty; L2 gain; Popov controller synthesis; bilinear matrix inequality; linear matrix inequality. 1

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. Iterative procedures are normally applied to a large class of robust control design problems in which the formulation naturally leads to bilinear matrix inequalities (BMIs). It is di cult to make concrete statements about the behavior of these 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 di culties exist for the new LMIbased iterative algorithm that we haverecently proposed to solve the BMIs that occur in robust H2 control design. The e ectiveness of the new algorithm has already been demonstrated on several numerical examples. This paper adds an important component tothediscussion on the convergence of the new algorithm by verifying that it e ciently 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 =Km-synthesis. 1