Research On Consistency Of Second-Order Delay Multi-Agent Systems

In recent decades,distributed cooperative control of multi-agent systems has attracted more and more research interest and the research directions of it involve various fields such as sensor networks,formation control,consensus problem,group synchronization,spacecraft attitude tracking control,distributed optimization calculation and control engineering.Consensus problem is the fundamental problem of the distributed cooperative control of multi-agent systems.Its goal is that a group of agents agree on a certain physical quantity based on local interaction rules.On the basis of the existing research,this paper considers the consensus problem of second order multi-agent system.Through the following two aspects of research:In the actual multi-agent system,due to many factors such as the limited information processing ability and communication range of the agent,errors and external uncertainties in the process of information transmission,time delay exists commonly in the process of multi-agent information interaction.Time delay not only affects the stability of multi-agent systems,but also leads to the undesirable behavior of agents and deteriorates the performance of agents to reach consensus.Delay-partitioning is regarded as an effective approach to reduce the conservatism of time-delayed systems.In the existing research of multi-agent systems with time delay,the applied delay-partitioning method is based on the idea of equal partition.The conservatism of the system could be reduced with the number of delay interval divisions increasing,but the computational complexity will increase.Therefore,a novel delay-partitioning method is applied to the multi-agent system with time delay to reduce the computational complexity.In order to further reduce the conservatism of the system,the integral term derived from the derivative of Lyapunov functional is effectively scaled based on the Wirtinger-based inequality and the reciprocally convex combination lemmas.For the conservatism of second-order multi-agent systems with time delay,there is still room for improvement of the Wirtinger-based inequality.In the process of stability analysis of multi-agent systems with time delay,the introduction of the second-order Bessel-Legendre inequality to amplify the integral term is smaller than the Wirtinger-based inequality.The second-order Bessel-Legendre inequality is closer to the true value of the integral term.In addition,in order to derive less conservative stability conditions,a triple integral term is added when constructing the Lyapunov functional.However,Wirtinger-based inequality cannot directly deal with the double integral term generated by the derivation of the triple integral.Therefore,the Wirtinger-based double integral inequality is introduced to solve this problem.Based on Lyapunov stability theorem and linear matrix inequality theory,the stability conditions that ensure the multi-agent agreement and less conservative are obtained.