The Consensus Of Discrete Multi-agent Systems With Asymmetric Delay

As a core problem of multi-agent systems, the consensus problem has made considerable progress up to now. In recent years, the study of multi-agent systems with delay are mostly based on symmetric delay and variable delay, but the study based on asymmetric delay has very few. In this paper, the consensus of discrete multi-agent systems which have asymmetric delay are discussed by us.The main contributions of this dissertation are summarized as follows:1. Under the network topology whose adjacency matrix is the stochastic matrix, the average consensus of discrete multi-agent systems with asymmetric delay. Using the theory of stochastic matrix and stability theory of discrete system, we respectively obtain the sufficient conditions of lyapnov stability and average consensus. Simulations are provided that demonstrate the effectiveness of our theoretical results.2. Under the network topology whose adjacency matrix is the stochastic matrix, the eigenvalue distribution consensus of discrete multi-agent systems with asymmetric delay. On the basis of predecessors’research, we propose the eigenvalue distribution consensus. Using the theory of stochastic matrix and stability theory of discrete system, we respectively obtain the sufficient condition of lyapnov stability and eigenvalue distribution consensus. Meanwhile we provide a new control protocol and a new algorithm which adjacency matrix of strongly connected graph Transform into the stochastic matrix, and ensure that as long as the network topology is strongly connected, under the new control protocol multi-agent systems can reach with eigenvalue distribution consensus.3.Under the network topology is a complete graph, the quantized average consensus of discrete multi-agent systems with asymmetric delay. Using the unique structure of complete graph, we respectively obtain that under different delay it is bounded between the states of multi-agent systems and the average state,and under the same delay the sufficient condition of quantized average consensus.Finally, a summary has been done for all discussions in the dissertation. The research works in future study are presented.