Consensus For High-order Linear Singular Multi-agent Systems

In recent fifty years,many scholars in the world have been attracted to the research on theory and application of singular multi-agent systems.Now,a great quantity progress has been made. With the development of the reseaech,it is found that many practical systems,such as mechanical systems,power systems,economic systems,robot systems and so on,belong to singular multi-agent systems.Singular multi-agent system,which is more suitable to describe a lot of practical systems than the regular system, particularly in engineering applications,have attracted a lot of attention,so research for it is of very important significance.The methods used mainly in this dissertation include matrix theory.Under conditions of directed graphs and output feedback,Consensus for high-order linear singular multi-agent systems with time delays are discussed respectively.The principal contributions are as follows:1.Consensus problems for high-order linear singular multi-agent systems with time delays on ditected graphs are dealt with.To eliminate impulse terms and ensure that the singular multi-agent systems can achieve containment, time-delayed protocols are presented for leaders and followers respectively.By model transformation,containment problems of singular multi-agent systems are converted into the stable problems of multiple low-dimensional systems.Sufficient conditions are submited in terms of linear matrix inequality,which are independent of the number of agents.Last,numerical simulations are expressed to demostrate theoretical results.2.Under output feedback consensus protocols with time delays,consensus problems for high-order linear singular multi-agent systems are investigated.First,the consensus problem is transformed into stable problems of mutiple singular subsystems by state decomposition.Then the sufficient condition of consensus are presented.Finally,numerical simulations are given to demostrate theoretical results.