Research On Consistency And Controllability Of Discrete Multi - Agent System

This paper studies the consensus problem and controllability of discrete time multi-agent systems, the main contents include:1.Some knowledge about graph theory and the related matrix in analysis of controllability and consensus problems are introduced firstly, and then some criteria or methods in analyzing the problems are proposed.2.The consensus of multi-agent systems without delay is analyzed. By the method of the Perron Frobenius theorem,discrete multi-agent system under general consensus form gets analysis.The consensus of multi-agent systems without delay is studied through Z transform and the Nyquist stability criterion. Finally, it analyzes consensus of discrete time multi-agent systems under the observer agreement by using matrix transformation and Gail circle theorem.3.The controllability of multi-agent system is studied in the paper. The controllability of first order system with single time-delay and multiple time delays is studied under the PBH criterion and the controlled conditions are given. And then it analyzes the controllability of double integrator discrete system, also under the two cases of single time delay and multiple time delays by using augmented matrix, determinant, controllable matrix to obtain controllable conditions.4.The controllability of the linear discrete-time multi-agent system is studied through the introduction of the controllability matrix sequence.It is also divided into two kinds,one kind is only with the state time delay, the other is with both state and input delays.Then the controllability of Leader-follower system switching topology is analyzed.Finally,example is given to illustrate the ideas and the corresponding results.