Networked Convergence of Fractional-Order Multiagent Systems with a Leader and Delay

Yuntao Shi,Junjun Zhang

doi:10.1155/2015/314985

Yuntao Shi, Junjun Zhang

Open Access

https://doi.org/10.1155/2015/314985

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Abstract

This paper investigates the convergence of fractional-order discrete-time multiagent systems with a leader and sampling delay by using Hermite-Biehler theorem and the change of bilinearity. It is shown that such system can achieve convergence depending on the sampling intervalh, the fractional-orderα, and the sampling delayτand its interconnection topology. Finally, some numerical simulations are given to illustrate the results.

Highlights

More and more scholars focus on the coordinated control [1, 2] of multiagent systems such as the consensus [3,4,5] and the controllability [6,7,8]
This paper investigates the convergence of fractional-order discrete-time multiagent systems with a leader and sampling delay by using Hermite-Biehler theorem and the change of bilinearity
The consensus of multiagent systems refers to the fact that agents in the system can transfer information and influence each other according to a certain protocol or algorithm, and eventually agents will tend to the consensus behavior with the evolution of the time in [17]

Summary

Introduction

More and more scholars focus on the coordinated control [1, 2] of multiagent systems such as the consensus [3,4,5] and the controllability [6,7,8]. Most of the practical distribution systems are fractional order [9,10,11,12]. With the development of society, fractional-order calculus theory [13,14,15,16] is widely used to study the signal processing and control, picture processing and artificial intelligence, and so on. In [19], the authors studied consensus of multiagent systems with heterogeneous delays and leader-following with integer-order and continuous time. In [20], the paper considered the consensus of fractionalorder multiagent systems with sampling delays without the leader. Some basic issues of fractional-order multiagent systems with time delay, such as the convergence, are still lacking in studying. We consider the convergence of fractionalorder discrete-time multiagent systems with a leader and sampling delay.

Preliminaries and Problem Statement

Main Results

Simulations

Conclusion