中国物理B ›› 2014, Vol. 23 ›› Issue (2): 20205-020205.doi: 10.1088/1674-1056/23/2/020205

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Exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and mode-dependent probabilistic time-varying delays

R. Rakkiyappana, N. Sakthivela, S. Lakshmananb   

  1. a Department of Mathematics, Bharathiar University, Coimbatore-641 046, Tamilnadu, India;
    b Department of Mathematical Sciences, College of Science, UAE University, Al Ain 15551, UAE
  • 收稿日期:2013-06-12 修回日期:2013-07-09 出版日期:2013-12-12 发布日期:2013-12-12
  • 基金资助:
    Project supported by the NBHM Research Project (Grant Nos. 2/48(7)/2012/NBHM(R.P.)/R and D Ⅱ/12669).

Exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and mode-dependent probabilistic time-varying delays

R. Rakkiyappana, N. Sakthivela, S. Lakshmananb   

  1. a Department of Mathematics, Bharathiar University, Coimbatore-641 046, Tamilnadu, India;
    b Department of Mathematical Sciences, College of Science, UAE University, Al Ain 15551, UAE
  • Received:2013-06-12 Revised:2013-07-09 Online:2013-12-12 Published:2013-12-12
  • Contact: R. Rakkiyappan, S. Lakshmanan E-mail:rakkigru@gmail.com;lakshm85@gmail.com
  • About author:02.30.Ks; 05.45.Gg; 05.45.Xt
  • Supported by:
    Project supported by the NBHM Research Project (Grant Nos. 2/48(7)/2012/NBHM(R.P.)/R and D Ⅱ/12669).

摘要: In this paper, the problem of exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and Mode-dependent probabilistic time-varying coupling delays is investigated. The sampling period is assumed to be time-varying and bounded. The information of probability distribution of the time-varying delay is considered and transformed into parameter matrices of the transferred complex dynamical network model. Based on the condition, the design method of the desired sampled data controller is proposed. By constructing a new Lyapunov functional with triple integral terms, delay-distribution-dependent exponential synchronization criteria are derived in the form of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

关键词: complex networks, exponential synchronization, mode-dependent time-varying delays, linear matrix inequalities, sampled-data control

Abstract: In this paper, the problem of exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and Mode-dependent probabilistic time-varying coupling delays is investigated. The sampling period is assumed to be time-varying and bounded. The information of probability distribution of the time-varying delay is considered and transformed into parameter matrices of the transferred complex dynamical network model. Based on the condition, the design method of the desired sampled data controller is proposed. By constructing a new Lyapunov functional with triple integral terms, delay-distribution-dependent exponential synchronization criteria are derived in the form of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

Key words: complex networks, exponential synchronization, mode-dependent time-varying delays, linear matrix inequalities, sampled-data control

中图分类号:  (Delay and functional equations)

  • 02.30.Ks
05.45.Gg (Control of chaos, applications of chaos) 05.45.Xt (Synchronization; coupled oscillators)