Robust Synchronization Of Linear Multi-agent Network Systems

The paper investigates the robust synchronization of multi-agent linear networksystems under time-varying and digraph structure．Over the last20years, synchrozationproblem has been popular subjects in systems and control, motivated by manyapplications in physics, social sciences, biology and engineering. The essence of thisproblem is the collective objective to reach agreement about some variables of interest.In the process of synchronizing the network systems, the whole systems would probablybe perturbed by the internal and external noises. Then one of the most importantproblems is whether the network systems can be synchronized by the same way it didbefore, i.e., what kind of condition the perturbation should be sufficed to make thesynchronization happen in the same way. This paper is trying to find out the condition tosynchronize the network systems under the given constant perturbation. The main resultis that the homogeneous and heterogeneous network systems with an additiveperturbation to the matrix of individual systems in the networks realize thesynchronization when this additive perturbation satisfies a given tolerance with themeans of norm presented in this paper．This paper has been organized by four chapters． Chapter one describes relativebackgrounds of the problems and introduction． Then some preliminaries and notions areprepared in chapter two． In chapter three, we prove the key lemma relative toperturbing matrix, and then we present how to realize the state and outputsynchronization in every details under the restriction of the perturbing matrix． And thenwe illustrate an example to testify the result of estimation of the perturbing matrix． Inlast chapter, we conclude the main results of this paper．...