Consensus with guaranteed convergence rate of high-order integrator agents in the presence of time-varying delays

Abstract

This paper aims to study the consensus problem in directed networks of agents with high-order integrator dynamics and fixed topology. It is considered the existence of non-uniform time-varying delays in the agents control laws for each interaction between agents and their neighbours. Based on Lyapunov–Krasovskii stability theory and algebraic graph theory, sufficient conditions, in terms of linear matrix inequalities, are given to verify if consensus is achieved with guaranteed exponential convergence rate. The efficiency of the proposed method is verified by numerical simulations. The simulations reveal that the conditions established in this work outperformed the similar existing ones in all numerical tests accomplished in this paper.

Keywords:

• consensus
• time-varying delay
• high-order systems
• Lyapunov–Krasovskii theory
• linear matrix inequalities

Additional information

Funding

This work was supported in part by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) [grant number 159879/2012-4] and [grant number 476530/2013-0]; Fundação de Amparo à Pesquisa do estado de Minas Gerais (FAPEMIG) [grant number TEC-APQ-02486-12] and [grant number TECAPQ-00735-13]; and Financiadora de Estudos e Projetos (FINEP) [grant number 0076/10].

Notes on contributors

H.J. Savino

Heitor J. Savino received his BS degree in mechatronic engineering from the Universidade do Estado do Amazonas, Brazil, in 2011 and his MSc degree in electrical engineering from the Universidade Federal do Amazonas, Brazil, in 2012. He is currently pursuing his Ph.D. degree at the Universidade Federal de Minas Gerais, Brazil. His research interests include consensus of multi-agent systems and time-delay systems.

F.O. Souza

Fernando O. Souza obtained his BS degree in control and automation engineering from the Pontifícia Universidade Católica de Minas Gerais, Brazil in 2003. He received his MS and Ph.D. degrees in electrical engineering at the Universidade Federal de Minas Gerais, Brazil in 2005 and 2008, respectively. He is presently an adjunct professor at the Department of Electronic Engineering, Universidade Federal de Minas Gerais, Brazil. His research interests are consensus of multi-agent systems, time-delay systems, and robust control.

L.C.A. Pimenta

Luciano C. A. Pimenta received his BS, MSc, and Ph.D. degrees in electrical engineering from the Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, Brazil, in 2003, 2005, and 2009, respectively. From April 2007 to June 2008, he was a visiting Ph.D. student at the General Robotics, Automation, Sensing and Perception (GRASP) Laboratory at the University of Pennsylvania, Philadelphia, USA. He is currently an assistant professor with the Department of Electronic Engineering at UFMG. His research interests include robotics, multi-robot systems, and control theory.