Leader-Following Consensus

This chapter studies the leader-following consensus problem. The study consists of two parts: The first focuses on a class of discrete-time nonlinear multiagent systems with time delay. Based on an asynchronous event-triggered mechanism, where local information of a communication graph is involved, a distributed consensus protocol is proposed to reduce the network communication congestion for achieving state consensus for multiagent nonlinear systems. Next, in the second part, we study the state consensus problem for linear shift-invariant homogeneous multiagent systems (MAS) over time-varying graphs. A novel approach based on the small gain theorem is proposed to design the consensus control protocols for both neutrally stable and neutrally unstable MAS, assuming the uniformly connected graphs. It is shown that the state consensus can be achieved for neutrally stable MAS under a weak uniform observability condition; for neutrally unstable MAS, the state consensus entails a strong uniform observability condition. Two numerical examples are worked out to illustrate our consensus results.