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This technical note 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 linear systems controlled through a communication network. We propose a new adaptive scheme with variable quantization step Δ, by defining an adaptation law exclusively in terms of information available at both the transmitter and receiver. With this approach, global asymptotic stability of the networked control system is achieved for a class of controllable (possibly unstable) linear plants. Moreover, thanks to the globally defined switching policy, this architecture enjoys a disturbance rejection property that allows the system to recover from any finite-time unbounded disturbance or communication loss.