Using increased order controllers in mixed H2/H∞ optimization

The problem of minimizing the 2-norm of one transfer function subject to an ∞-norm bound on another transfer function is examined for increased order controllers. It is shown that, unlike controllers under full-state availability, output feedback controllers are unable to achieve the global minimum 2-norm while simultaneously meeting the ∞-norm constraint for certain levels of γ, regardless of compensator order. The solution to the mixed H₂/H_∞, problem is shown to lie on the boundary of the ∞-norm constraint in the increased order case for this same range of γ´s. Also, it is shown that the optimal compensator order for the mixed problem is greater than the order of the plant under certain conditions. A numerical example is given.