Design of optimal mixed H2/H∞ static state feedback controllers

Despite advances in robust control theory, the robust performance problem formulated in the mixed H₂/H_∞ framework largely remains an open problem. In this approach, one seeks a controller that minimizes the H₂ norm of a closed-loop map over all admissible controllers while satisfying an H_∞ constraint on another closed-loop map. Unlike the optimal H₂ problem or the γ-level sub-optimal H_∞ problem, the mixed H₂/H_∞ problem does not have a readily computable solution. In the paper we restrict consideration to static state feedback controllers and propose an efficient iterative algorithm for computing the optimal H₂/H_∞ solution