Invariant set based distributed protocol for synchronization of discrete-time heterogeneous systems with nonlinear dynamics

We in this paper propose an invariant set based distributed control protocol for synchronization of discrete-time heterogeneous multiagent systems. Starting with the assumption that the distributed control input will vanish once a multiagent system achieves synchronization, we attain an easily verifiable method for the nonexistence of synchronous trajectories through characterizing the vector fields of agents. Then, we introduce an invariant set to analyze the limit behaviors of all the synchronous trajectories. Afterwards, based on the assumption that the above invariant set can be characterized by the graph of a function, we design a distributed control protocol to transform the heterogeneous system into an equivalent one, which is composed of two lower dimensional systems. Moreover, for this equivalent system, we provide a synchronization criterion via constructing corresponding Lyapunov-type functions for these two lower dimensional systems, arriving at a synchronization criterion for the original heterogeneous system. Especially, we further improve the applicability of this synchronization criterion by using multiple Lyapunov-type functions. Finally, three examples are presented to demonstrate the validity of the corresponding theoretical results.