An absorption heat pump system is a complex nonlinear system. The system dynamics varies considerably depending on the load. The local linearization technique is not suitable for such a system, because a linearized model approximates the original nonlinear system only in the neighborhood of the point where linearization is done. In this paper, the dynamics of an absorption heat pump system is modelled as a linear time-varying system, of which the system matrix is within a specified polytope at any time. Once a plant is modelled as a polytope system, a controller design problem can be reduced to a convex programming problem which can be solved easily. Numerical simulations illustrate that this procedure is practical and effective to design a load following controller for the absorption heat pump system.