Quantized Near-Consensus via Quantized Communication Links

This paper develops a framework for treating multiagent consensus problems using quantized control. Specifically, we present asymmetrically and symmetrically quantized consensus protocols for multiagent dynamical systems. The proposed consensus protocols involve the exchange of quantized information between agents. Due to quantization, the requirement for consensus is weakened to quantized near-consensus, Under certain assumptions on the network topology, the proposed protocols guarantee that the closed-loop dynamical network is Lyapunov stable and convergent to an appropriately defined set in finite time. We present a complete stability and convergence analysis, using graph theory and nontangency-based Lyapunov tests. The robustness of the symmetrically quantized consensus protocols to slowly-varying communication errors is analyzed. To our knowledge this is the first time such an analysis has been presented in the literature. Several simulation examples illustrate the main results of the paper.