Leader-Following Protocol Design for Switched Multiagent Systems with Randomly Occurring Self-Delay

M J Park,Ju H Park,E J Cha,S M Lee,O M Kwon

doi:10.1155/2013/726198

Abstract

This paper designs a delay-dependent leader-following protocol for multiagent systems with both communication delay and randomly occurring self-delay. Based on the randomly occurring mode of self-delay, a new model of switched multi-agent systems which have not been introduced yet is constructed. By constructing a newly piecewise Lyapunov-Krasovskii functional, a leader-following stability criterion of the switched multi-agent systems is derived by the framework of linear matrix inequalities (LMIs) and the average dwell time with the randomly occurring mode. Based on the result of the derived stability criterion, a designing leader-following protocol for the system will be proposed. One numerical example is included to show the effectiveness of the proposed method.

Highlights

During the last few years, Markovian jumping mode [1, 2], the randomly occurring mode with probabilistic property [3,4,5], the average dwell time approach [6,7,8,9], the indicator function definition with arbitrary mode [10], and other changing or switching signal modes are being put to treat in the various systems with changing or switching parameters
(i) It is a well-known fact that when all linear systems in the family ẋ(t) = Apx(t), p ∈ P = {1, 2, . . . , m} are stable, the switched linear system ẋ(t) = Aσ(t)x(t), where σ(t) is switching signal, is stable if the dwell time is sufficiently large [6]
Before introducing Theorem 12, some notations will be defined for simplicity of matrix representation. θi ∈ R5Nn×Nn (i = 1, 2, . . . , 5) are defined as block entry matrices; for example, θ3 = [0Nn⋅2Nn, INn, 0Nn⋅2Nn]T

Summary

Introduction

During the last few years, Markovian jumping mode [1, 2], the randomly occurring mode with probabilistic property [3,4,5], the average dwell time approach [6,7,8,9], the indicator function definition with arbitrary mode [10], and other changing or switching signal modes are being put to treat in the various systems with changing or switching parameters. Multi-agent systems (MASs) [11] have received considerable attention due to their extensive applications in many fields such as distributed sensor networks [12], vehicle systems [13, 14], groups of mobile autonomous agent [15], multi-agent robotic system [16], and other applications [17,18,19] Before handling this system, since modern systems use information between each agent in networks, these days, we need to pay keen attention to the three following considerations

Objectives

Results

Conclusion