Distributed Interval Observer-Based Consensus Control for Discrete-Time Multiagent Systems

This article investigates distributed consensus control for discrete-time multiagent systems with unmeasurable states and bounded disturbances under undirected topologies. To reconstruct the system states and attenuate disturbance effects, two classes of distributed interval observers (DIOs) are developed: the monotone system theory-based DIO (MTDIO) and the interval hull-based DIO (IHDIO). Building on these DIOs, corresponding consensus control protocols are proposed, including a general consensus protocol and a robust$H_{\infty }$consensus control protocol. Stability conditions for the error dynamics are derived via linear matrix inequalities. Simulation results demonstrate the effectiveness of the proposed strategies. Compared to the MTDIO approach, the IHDIO-based$H_{\infty }$scheme achieves significantly tighter interval estimates and higher control accuracy, albeit at the cost of increased computational complexity.