## Convergence Analysis of A Parametric Robust H 2 Controller Synthesis Algorithm

### BibTeX

@MISC{Banjerdpongchai_convergenceanalysis,

author = {David Banjerdpongchai and Jonathan P. How},

title = {Convergence Analysis of A Parametric Robust H 2 Controller Synthesis Algorithm },

year = {}

}

### OpenURL

### Abstract

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 difficult 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 difficulties exist for the new LMI-based iterative algorithm that we have recently proposed to solve the BMIs that occur in robust H2 control design. The effectiveness of the new algorithm has already been demonstrated on several numerical examples. This paper adds an important component to the discussion on the convergence of the new algorithm by verifying 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/Km-synthesis.