The Consensus Problem Of Multi-Agent Systems With Sampled-data

Recently,distributed coordination control of multi-agent systems have been attracting serious concern of researchers.This is mainly because of its numerous extensive applications such as sensor networks,formation control,computer control and social science,etc.Among the major areas of coordination control of multi-agent systems,consensus is one of the most significant and fundamental problems,which aims to design the distributed protocol such that the final states of all agents can converge to an agreement.Meanwhile,in many practical applications,due to the application of digital sensors and controllers,agents might only communicate with their neighbors periodically rather than continuously.Thus,the study on sampled-data control has increasingly attracted.This paper studies the consensus problem of continuous-time general linear multi-agent systems and second-order multi-agent systems with sampled-data.Firstly,we discuss the sampled-data consensus problem of multi-agent systems based on a continuous-time model,and the interaction topology is assumed to be undirected,then,a distributed sampled-data consensus protocol was proposed to solve the consensus problem.Different from the discrete-time approach and the input delay approach,this paper does not considering the states in the sampling periods,which the decrease of Lyapunov function is guaranteed only at each sampling instants.By virtue of the Lyapunov method,a sufficient condition is obtained in terms of linear matrix inequalities,by which LMI-based approach was proposed to solve the feedback gain matrix.Secondly,we investigate the consensus problem with position sampled-data for second-order multi-agent systems,and the interaction topology among the agents is depicted by a directed graph.The fullorder and reduced-order observers with position sampled-data are proposed,by which two kinds of sampled-data based consensus protocols are constructed.With the provided sampled protocols,the consensus convergence analysis of continuous-time multi-agent system is equivalently transformed into that of a discrete-time system.Then,some sufficient and necessary consensus conditions about coupling parameters and sampling period are obtained with the help of matrix and sampled control theory.