Consensus control for networks of agents with fixed topology and quantized communication

In this paper, without assuming balanced network topologies, we address the weighted average consensus problem for discrete-time single-integrator multi-agent systems with logarithmic quantized information communication. By incorporating the generalized quadratic Lyapunov function with the discrete-time Bellman-Gronwall inequality, a new upper bound about the quantization precision parameter of the infinite-level logarithmic quantizer is derived to design quantized protocol, under which agents in strongly connected directed networks can attain weighted average consensus. The obtained new upper bound clearly characterizes the intimate relationship between the quantization precision parameter and the directed network topology property. The proposed quantized protocol takes the joint effects of information quantization and network topology into consideration, and therefore, it is in particular applicable to digital networks where bidirectional and/or balanced message passing among agents is not available.