For an absorption heat pump system, the authors have proposed a controller design method, in which the dynamical behavior of the system is approximated by a linear differential inclusion so that the nonlinearity of the system can be taken into account in controller design. However, this method has two problems. Namely, the controller obtained by this method＇ tends to be high-gain and the closed-loop system with the controller tends to have a small decay rate. In this paper, we propose an improved controller design method, in which some constraints are added to the controller specification to cope with the problems mentioned above. The necessary and sufficient conditions for the design problem with multiple specifications are solved by the algorithm that we developed recently.