Tracking Consensus for Linear Multi-Agent Systems with Exponential Convergence Rate

This paper discusses the leader-following consensus problem of a group of homogeneous linear multi-agent systems. The control input of the leader is possibly nonzero and known to all the agents in the network. To ensure tracking, a dynamic control law is developed based on the relative information of actual states and internal controller states of neighbouring agents. Under the proposed framework, the tracking of multi-agent systems having no exponentially unstable mode is first achieved and then a generalized control law is postulated when systems posses exponentially stable or unstable modes. By the proposed dynamic control law, no information of the Laplacian matrix is needed when systems do not posses any exponentially unstable mode. However, this sort of information is needed to design the coupling strength in the presence of unstable modes in agent dynamics. The rate at which the error between the states of the agents and the leader trajectory decay has been resolved. Illustrative examples are provided to demonstrate the efficacy of the dynamic control.