Consensus Problem In Multi-Agent Systems With Random Time-Delay

:In recent years, with the rapid development of science and application, cooperative control of multi-agent systems has become a hot research in the field of control.As the basis of the coordination problem for multi-agent systems,the consensus problem has attracted more and more attentions.In the multi-agent systems,consensus means that all the states of the multi-agent systems reach at the same values,and consensus algorithm is the rules of interaction between each agent. In this paper, we focus on the consensus problem for multi-agent systems with algebraic graph theory,matrix theory,Lyapunov stability theory and the method of linear matrix inequalities.The main research contents and results are summarized as follows:1. Consensus in multi-agent systems with random time-delay. First the problem of average consensus is studied, then some sufficient criteria for achieving the average consensus via the suggested algorithm are derived with using Lyapunov function and LMI method. Secondly, consensus in multi-agent systems with leader-following and random time-delay, some sufficient criteria for achieving the consensus via the suggested algorithm are derived with using Lyapunov stability analysis and stochastic analysis method, finally simulations are given to verify the correctness of the results.2. Consensus in multi-agent systems with random time-delay and external perturbations. The consensus problem of the multi-agent systems is converted into robust consensus, some sufficient criteria for achieving the consensus via the suggested algorithm are derived with using Lyapunov stability analysis and the method of linear matrix inequalities in the case of fixed network topology and switching network topology. Finally, simulations are given to verify the correctness of the algorithm.3. Finite-time consensus of multi-agent systems with leader-following and random time-delay. By introducing a consistency gain matrix and desgning a finite-time consistency control algorithm, some sufficient criteria for achieving the finite-time consensus via the suggested algorithm are derived with using finite-time Lyapunov stability analysis and stochastic analysis method to achieve a limited time consistency of the maximum communication delay upper bound. Finally, simulations are given to verify the correctness of the algorithm.