This paper investigates the closed-loop properties of the differential coding scheme known as Delta-modulation (Δ-M) when used in feedback loops within the context of feedback controlled systems. We propose a new modified scheme of the original form of the Δ-M algorithm which is better suited for applications where the sensed information is used in feedback. A state feedback controller is implemented with the state estimated by a predictor-based differential decoder. Stability of the resulting closed-loop system (controller-coder-decoder) is studied. These properties (stability and performance) depend on the quantization parameter Δ, which is assumed constant in the first part of this paper. In a further step, parameter Δ is made adaptive, by defining an adaptation law exclusively in terms of information available at both the transmitter and receiver side.With this approach both stability and performance is improved.