An iterative method for mixed H2/H∞ synthesis via static output-feedback

The mixed H₂/H_∞ problem is an open problem whose closed-form solution is not known except for special cases presented in the literature. After the problem definition and a short survey of some general existing results, a new sufficient condition for the mixed synthesis problem via static output feedback is proposed. This new sufficient condition relies on the introduction of new extra variables leading to the use of two different Lyapunov functions. This allows us to reduce the conservatism of the usual existing conditions. A coordinate-descent based iterative numerical procedure is used to compute local optimal solutions of the initial problem. The relevance of this approach is illustrated by a numerical example.