Design of optimal mixed H_2/H_∞ static state feedback controllers

Abstract

Despite advances in robust control theory, the robust performance problem formulated in the mixed H_2/H_∞ framework largely remains an open problem. In this approach, one seeks a controller that minimizes the H_2 norm of a closed-loop map over all admissible controllers while satisfying an H_∞ constraint on another closed-loop map. Unlike the optimal H_2 problem or the γ-level sub-optimal H_∞ problem, the mixed H_2/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 H_2/H_∞ solution.