Linearly combined suboptimal mixed H2/H∞ controllers

In this paper we consider the problem of minimizing the H₂ 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 H₂/H_∞ problem by restricting the search to a class of linearly combined controllers. Such mixed linearly combined controllers yield smaller closed-loop H₂ 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 H₂ controller satisfies the H_∞ bound