Robust Consensus of Double‐Integrator Agents With Input Saturations and Disturbances Using Duplex PI Control Laws

In this article, we study leader‐following and leaderless consensus problems for double‐integrator agents subject to input saturations and constant disturbances. To address these problems, we propose duplex proportional‐integral control laws that are constructed over two independent communication graphs. We then derive sufficient conditions for achieving consensus under input saturations and constant disturbance in both leader‐following and leaderless cases. The analysis shows that only the communication graph of the integral control law needs to be connected, while the proportional control network needs to be sparsely connected or even omitted. This duplex structure provides flexibility in network design and reduces communication overhead. Finally, we provide numerical examples to demonstrate the validity and effectiveness of the proposed control laws.