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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2016, Vol. 33 ›› Issue (1): 73-90.doi: 10.3969/j.issn.1005-3085.2016.01.008

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模型依赖时变时滞马尔可夫跳变复杂网络的混合投影同步(英)

邵浩宇1,  胡爱花1,  胡满峰1,2   

  1. 1- 江南大学理学院，无锡 214122
    2- 江南大学轻工业先进控制重点实验室(教育部)，无锡 214122
  • 收稿日期:2014-09-30 接受日期:2015-04-17 出版日期:2016-02-15 发布日期:2016-04-15
  • 基金资助:
    国家自然科学基金 (11202084).

Hybrid Projective Synchronization of Markovian Jumping Complex Networks with Mode-dependent Time-varying Delays

SHAO Hao-yu1,  HU Ai-hua1,  HU Man-feng1,2   

  1. 1- School of Science, Jiangnan University, Wuxi 214122
    2- Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122
  • Received:2014-09-30 Accepted:2015-04-17 Online:2016-02-15 Published:2016-04-15
  • Supported by:
    The National Natural Science Foundation of China (11202084).

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摘要： 复杂网络的混合投影同步已广泛应用于工程、应用数学等各个领域．本文研究了一类模型依赖时变时滞的马尔可夫跳变复杂网络的混合投影同步问题．另外，对于复杂网络中的每个响应系统，同时考虑了线性耦合和非线性耦合．基于李雅普诺夫稳定性理论和线性矩阵不等式方法，推导出复杂网络混合投影同步的充分条件．数值仿真最后证明了所提理论的有效性．本文的结果为研究复杂网络的混合投影同步和模型依赖时变时滞系统的控制提供了理论依据．

关键词: 混合投影同步, 马尔可夫跳变, 时变时滞, 复杂网络

Abstract:

Hybrid projective synchronization of complex networks has recently been applied to various areas of engineering, applied mathematics and others. In this paper, the problem of hybrid projective synchronization for a class of Markovian jumping complex networks with mode-dependent time-varying delays is investigated. Linear coupling function and nonlinear coupling function are considered simultaneously for each response system in complex networks. Based on Lyapunov stability theory and linear matrix inequality method, some sufficient conditions for hybrid projective synchronization of complex networks are derived. Numerical simulations are finally demonstrated to illustrate the effectiveness of the developed theory. The results provide theoretical basis for hybrid projective synchronization of complex networks and control of system with mode-dependent time-varying delays.

Key words: hybrid projective synchronization, Markovian jumping, time-varying delays, complex networks

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