Convergence Of Linear Multi-agent Systems With Leaders

Consensus of multi-agent systems(MASs)is a typical and basic problem in distributed coordination of MASs.As two important generalizations of consensus problem,bipartite consensus and cluster consensus are more general.In this paper,these two problems for leader-following MASs described by two typical linear dynamics,i.e.the first-order integrator and high-order linear time-invariant systems,are studied.The main results are as follows:1.Leader-following bipartite consensus problem for the first-order integrator MASs with disturbance is studied.The influence of disturbance on leader-following bipartite consensus is studied.An observer is designed for each follower,and then composite bipartite consensus protocols are presented with/without external disturbance.It is proven that if the communication topology of the MAS consisting of leader and followers is structurally balanced and contains a spanning tree,then by the proper choice of gain constants satisfying certain conditions,the MAS can achieve leader-following bipartite consensus under the proposed protocols regardless of external disturbance.2.Leader-following cluster consensus problem for high-order linear MASs is studied.State feedback and output feedback control protocols are designed for each follower,respectively.By using the tools from algebraic Riccati equation and matrix analysis,sufficient conditions for leader-following cluster consensus are given.It is shown that if the communication topology of the MAS composed of leader and followers is interactively balanced and contains a spanning tree,then by properly selecting control gains,the MAS can achieve leader-following cluster consensus under the given control protocols.Particularly,it is found that the leader-following cluster consensus problem based on output feedback protocol can be transformed into a static output feedback problem by means of an error system.If the input and output matrices of the follower satisfy a certain rank condition,then the MAS can achieve leader-following cluster consensus under the designed output feedback control protocol.