A Unified Approach to Practical Consensus with Quantized Data and Time Delay

In this paper, we study the consensus problem of multi-agent networks subject to communication constrains. Undirected and weighted network is considered here. Two types of communication constrains are discussed in this paper: i) each agent can only exchange quantized data with its neighbors and ii) each agent can only obtain the delayed information from its neighbors. The main contribution of this paper is to provide a precise mathematical treatment for the continuous multi-agent network with quantization and time delay. The existence of a global solution to the resulting system is firstly proved in the Filippov sense and then we prove that the solution converges to a practical consensus set asymptotically. Here, practical consensus means that the final consensus values are bounded within an interval, but not a value. Further, an explicit relationship among time delay, quantization parameter and the practical consensus set are theoretically presented. Numerical examples are finally given to demonstrate the effectiveness of the obtained theoretical results.