High-order Linear Multi-agent Systems Are Based On The Convergence Of State Observers

This paper considers consensus problem of high-order linear multi-agent systems.In view of the physical unrealizability of state feedback,a new type of state observer control protocol is designed for each agent,whose dynamics is extended to linear time-invariant systems.Based on them,sign-consensus and cluster consensus are investigated in this paper.Main results are as follows.1.Sign-consensus of high-order linear multi-agent systems is studied.By using the output and input of agents,the state is estimated,and a state observer type control protocol is designed for each agent.By using the tools of matrix analysis and ordinary differential equation theory,the closed-loop system is analyzed.It is proven that if the adjacency matrix of the graph has strong Perron-Frobenius property or is finally positive,then the high-order linear multi-agent system can achieve sign-consensus.2.Cluster consensus of high-order linear multi-agent systems is studied.A weighted digraph is employed to represent the interactions of agents.A type of state observer protocols are designed for agents.It is proven that if the weighted digraph contains a spanning tree,then under some mild conditions,the high-order linear multi-agent systems can achieve cluster consensus.Particularly,traditional consensus and bipartite consensus can be regarded as its special cases.