Admissible Consensus Of Discrete-time Descriptor Multi-agent Systems

Along with the deepening research of modern control theory as well as the penetration to other disciplines such as aerospace、chemical、petroleum、aviation、network and communications and so on,it was found that a class of more valuable systems, namely, descriptor systems. Among them, descriptor multi-agents systems successfully attract the attention of many experts and scholars, and the basic problem is that to set up its mathematical model and solve related consensus problems. The general steps to solve the consensus problem of system is to design a feasible algorithm, then constructs the agreement protocol, finally, the system can achieve asymptotic consensus even agreement.In this paper, we considered the consensus problem of descriptor multi-agent systems. Each agent’s dynamics is given in general form of continuous-time linear descriptor system, under the condition of fixed topology,we assumed the communication topology among the agents is directed while in the case of switching topology is assumed to be balanced. In order to solve the consensus problem of multi-agent systems, we proposed two kinds of distributed consensus protocols based on state disagreement and output disagreement for each agent,respectively. In order to design the gain matrices involved in the protocol,we provided a multi-step algorithm to obtain it by solving the generalized Riccati equations. At the same time,in order to guarantee the descriptor multi-agent system can achieves consensus, we established some sufficient consensus conditions. Furthermore, the protocol not only can be generalized to solve leader-following consensus problem but also established the similar consensus condition. Finally, for the sake of illustrate our obtained results is effective,we provided a simulation example.