LMI-based algorithms for frequency weighted optimal H2-norm model reduction

In this paper, algorithms based on the matrix inequality framework are derived to solve the frequency weighted optimal H₂ norm model reduction problem. As this problem involves a bilinear matrix inequality and thus is not directly solvable, two steps iterative schemes are used to approach the solution. The key-point of the paper is as following: it is shown how to use two different formulations of the problem to obtain a final algorithm that should avoid getting stuck into local minima and thus converge to the global solution. All proposed algorithms revealed a good behavior on several classical examples, whereas no demonstration has yet been found