Linearly Combined Suboptimal Mixed H_2/H_∞ Controllers

In this paper we consider the problem of minimizing the H_2 norm of a closed-loop map over all static state feedback controllers while satisfying an H_∞ constraint on another closed-loop map. We propose a readily computable suboptimal solution to the pure mixed H_2/H_∞ problem by restricting the search to a class of linearly combined controllers. Such mixed linearly combined controllers yield smaller closed-loop H_2 norms than those obtained by using the central solutions of the H_∞ problem. Moreover, the mixed controllers achieve the optimal H2 performance whenever the optimal H_2 controller satisfies the H_∞ bound