This paper presents a complete solution to an extended H-infinity control problem for a generalized plant comprising a physical system cascaded with weights containing poles in the closed right half-plane. Necessary and sufficient conditions for a solution to exist are obtained which guarantee closed-loop stability of the physical system and controller as well as achieving the H-infinity norm constraint on the closed loop of the transfer function matrix of the generalized plant and controller interconnection. The set of all feasible controllers is characterized. Conditions for solvability are a minimal variation on those appearing in the standard H-infinity control problem.