  In this paper we consider a class of linear time invariant systems with
infinitely many unstable modes. By using the parameterization of all
stabilizing controllers, we show that H-infinity controllers for such systems
can be computed using the techniques developed earlier for infinite dimensional
plants with finitely many unstable modes. We illustrate connections between the
problem solved here and an indirect method for strongly stabilizing H-infinity
controller design for systems with time delays.
