Distributed Consensus Algorithm and Stability for LTI Multi-Agent Systems on Directed Graphs

This paper focuses on the fully-distributed consensus algorithms for a class of multi-agent systems on directed graphs, where every agent can be described by high-order linear time invariant (LTI) dynamics. Firstly, a novel consensus algorithm is proposed for the multi-agent systems. Then, taking use of the complex variable theories of linear multivariable feedback systems, the consensus and stability proof of the closed systems is proved. In the algorithm and proof, the complex roots are permitted in closed-loop characteristic equation of agents, which relaxes some assumptions commonly considered in the available literatures, such as real roots. Furthermore, the constraint condition for them is given, which is one of the key factors to guarantee the stability of the whole systems. Moreover, designing and proof of the consensus show that the same in dimension among agents is not necessary at all, which provides another convenience for researching multi-agent systems. Simulation results are provided to illustrate the effectiveness of the proposed approach.