Robust Controller Design by Output Feedback against Uncertain Stochastic Disturbances

We consider the problem of minimizing the worst asymptotic output variance of a control system if the disturbances are restricted to set-constraints on their covariance coefficients only. We reveal how one simple Lagrange duality argument allows the re-formulation as a parameterized positive real design problem. As the main contribution, we provide a direct solution of this parameterized positive real design problem for general LTI systems in terms of linear matrix inequalities. This renders the output-feedback controller design problem against uncertain stochastic signals amenable to numerically efficient algorithms.