Optimal strictly positive real controllers using direct optimization

In this paper, we consider the H2-optimal control problem subject to the constraint that the resulting controller be strictly positive real. A direct numerical optimization approach is adopted in conjunction with a controller parametrization that is linear in the unknown parameters. The SPR constraint is easily expressed at each frequency in the form of a linear inequality. The method is applied to a numerical example from the literature and good results are achieved. In particular, the proposed method is particularly adept at determining low order controllers.