In this paper, H-infinity control for a class of linear time invariant systems with infinitely many unstable poles is studied. An example of such a plant is a high gain system with delayed feedback. We formulate the problem via a generalized plant which consists of a rational transfer matrix and the inverse of a scalar (possibly irrational) inner function. It is shown that the problem can be decomposed into a finite-dimensional H-infinity control problem and an additional rank condition. (C) 2007 Elsevier B.V. All rights reserved.