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In this paper, we consider the quantized consensus problem of multiple discrete-time integrator agents which suffer from additive noise. Due to the limited communication resources, each agent can only exchange quantized information of finite length with its neighbors through unreliable channels, where the transmitted signals may be delayed or even lost. Quantization errors, network delay, and packet loss result in quantization mismatch. To handle the additive noise and quantization mismatch, a quantized consensus protocol is proposed by implementing dynamic encoding and decoding policies at a finite bit rate. Particularly, the proposed consensus protocol introduces an internal saturation function into all the controllers of agents so that the control inputs of neighbor agents can be predicted locally by each agent even under distributed control law and quantization mismatch. Based on such shared control input information, the proposed consensus protocol can guarantee the achievement of the approximate consensus of all agents in the input-to-state sense, i.e., the consensus errors of agents are bounded from above by the sum of a class  $\mathcal {K}_\infty $  function of the upper bound of the additive noise and a class  $\mathcal {KL}$  function of the upper bound on the initial states of agents. It is shown that such approximate consensus in the input-to-state sense can be guaranteed at an as low bit rate as 1 bit per time step for each agent without requiring any global information, except an upper bound of the number of agents. Two specific situations, namely packet loss, and network delay, are further analyzed with the explicit expressions of quantization mismatch. The simulations are done to confirm the effectiveness of the proposed quantized consensus protocol.

Robust Quantized Consensus of Discrete Multi-Agent Systems in the Input-to-State Sense