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Volume 2018, Article ID 8546304, 13 pages
Research Article

Finite-Time Nonfragile Synchronization of Stochastic Complex Dynamical Networks with Semi-Markov Switching Outer Coupling

1Department of Mathematics, Bharathiar University, Coimbatore 641046, India
2Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea
3Department of Mathematics, Anna University Regional Campus, Coimbatore 641046, India
4Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China
5Department of Applied Mathematics, Kongju National University, Chungcheongnam-do 32588, Republic of Korea

Correspondence should be addressed to Yong-Ki Ma;

Received 13 July 2017; Accepted 14 December 2017; Published 16 January 2018

Academic Editor: Hiroki Sayama

Copyright © 2018 Rathinasamy Sakthivel et al. 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.


The problem of robust nonfragile synchronization is investigated in this paper for a class of complex dynamical networks subject to semi-Markov jumping outer coupling, time-varying coupling delay, randomly occurring gain variation, and stochastic noise over a desired finite-time interval. In particular, the network topology is assumed to follow a semi-Markov process such that it may switch from one to another at different instants. In this paper, the random gain variation is represented by a stochastic variable that is assumed to satisfy the Bernoulli distribution with white sequences. Based on these hypotheses and the Lyapunov-Krasovskii stability theory, a new finite-time stochastic synchronization criterion is established for the considered network in terms of linear matrix inequalities. Moreover, the control design parameters that guarantee the required criterion are computed by solving a set of linear matrix inequality constraints. An illustrative example is finally given to show the effectiveness and advantages of the developed analytical results.