In this paper, we consider design of interconnected H-inf feedback control systems with quantized signals. We first assume that a decentralized state feedback has been designed for an interconnected continuous-time LTI system so that the closed-loop system is stable and a desired H-inf disturbance attenuation level is achieved, and that the subsystems states are quantized before they are passed to the local controller. We propose a local-state-dependent strategy for updating the quantizers parameters, so that the overall closed-loop system is asymptotically stable and achieves the same H-inf disturbance attenuation level. We then extend the result to the case of decentralized static output feedback where the measurement outputs are quantized, and propose a local-output-dependent strategy for updating the quantizers parameters. Both the pre-designed controllers and the quantizers parameters are constructed in a decentralized manner, depending on local information.