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Journal of Control Science and Engineering
Volume 2017, Article ID 7937916, 9 pages
Research Article

Distributed Optimization of Multiagent Systems in Directed Networks with Time-Varying Delay

College of Science, China Three Gorges University, Yichang 443002, China

Correspondence should be addressed to Hui Yu; nc.ude.ugtc@iuhuy

Received 3 January 2017; Revised 19 February 2017; Accepted 16 March 2017; Published 29 March 2017

Academic Editor: Chaojie Li

Copyright © 2017 Junxiu Yan and Hui Yu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper addresses a distributed consensus optimization problem of a first-order multiagent system with time-varying delay. A continuous-time distributed optimization algorithm is proposed. Different from most ways of solving distributed optimization problem, the Lyapunov-Razumikhin theorem is applied to the convergence analysis instead of the Lyapunov-Krasovskii functionals with LMI conditions. A sufficient condition for the control parameters is obtained to make all the agents converge to the optimal solution of the system. Finally, an example is given to validate the effectiveness of our theoretical result.