Consistency Of High-order Linear Time-delay Multi-agent Systems

Since 1970 s,the research on multi-agents has received widespread attention from scholars at home and abroad with the rapid development of communication,computing and control theory.In this paper,basing on directed graphs and unpredictable systems,the consensus problem of multi-agent systems is studied for two classes in the presence of input delay.Firstly,regardless of the leader's input,the consensus of containment problem is investigated only for followers in the presense of bounded and time-varying input.Secondly,the consensus of containment problem is studied for a class of multi-agent systems with leaders having external disturbance inputs and followers having mixed delay protocol inputs in the presence of Lipschitz nonlinear terms.The main results of the paper will be given from the following aspects:1.In chapter 3,the consensus of containment problem is investigated for a class of multiagent systems with leaders having zero input and followers having unpredictable states in the presence of the controller containing a bounded constant delay input.Firstly,according to the assumption that the relative output of the system is measurable,the observer and controller of the followers are designed at the same time.The form of observer feedback is used in control input and the designed observers consist of relative state output among agents.Then,by constructing suitable Lyapunov-Krasovskii functionals and using Matlab software to solve corresponding linear matrix(LMIs)inequalities,which obtained the conditions of consensus.Finally,the actual simulation examples are provided to illustrate the correctness of theory by using Simulink software.2.Basing on chapter 3,in chapter 4,the consensus of containment problem is investigated for a class of multi-agent systems with leaders having zero input and followers having unpredictable states in the presence of the controller containing a time-varying time-delay input.Firstly,according to the assumption that the observer and controller of the followers are designed at the same time.Then,by constructing suitable Lyapunov-Krasovskii functionals and using Matlab software to solve corresponding linear matrix(LMIs)inequalities,which obtained the conditions of consensus.Finally,the actual simulation examples are provided to illustrate the correctness of theory by using Simulink software.3.In chapter 5,the consensus of containment problem is investigated for a class of multiagent systems with leaders having external disturbance input and followers having mixed delay protocol inputs in the presence of the controller containing a time-varying time-delay inputs.Specifically,the systems considered in this paper are unpredictable and containing non-linear terms.Firstly,according to the assumption that the observer and the controller of the leaders and followers are designed separately.The non-linear functions are introduced in the follower's controller design,which are utilized to eliminate the effects of the leader's non-zero disturbance input.Next,the design algorithms for the gain of the observer and controller are given.Then,by constructing suitable Lyapunov-Krasovskii functionals and using Matlab software to solve corresponding linear matrix(LMIs)inequalities,which obtained the conditions of consensus.Finally,the actual simulation examples are provided to illustrate the correctness of theory by using Simulink software.