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Nonlinear Dynamics

, Volume 95, Issue 3, pp 2031–2062 | Cite as

Global synchronization in fixed time for semi-Markovian switching complex dynamical networks with hybrid couplings and time-varying delays

  • Zhibo Wang
  • Huaiqin WuEmail author
Original Paper

Abstract

This paper is concerned with the global synchronization in fixed time for semi-Markovian switching complex dynamical networks with hybrid couplings and time-varying delays in the presence of disturbances. Firstly, the property with respect to the global stability in fixed time is developed for semi-Markovian switching nonlinear systems. Subsequently, a novel sliding manifold with double integration is presented based on the proposed principle of convergence in fixed time. Under the designed sliding mode controller, the state trajectory of synchronization error system is driven to the prescribed sliding manifold in fixed time. In addition, the global stability in fixed time of sliding mode dynamics is proved analytically. By means of the stochastic Lyapunov–Krasovskii functional approach, the synchronization condition is established in terms of linear matrix inequalities; moreover, the stochastic fixed settling-time can be determined to any desired values in advance, via the configuration of parameters in the proposed controller. Finally, two numerical examples are provided to demonstrate the validity of the theoretical results and the feasibility of the proposed approach.

Keywords

Complex dynamical networks Fixed-time synchronization Semi-Markovian switching Sliding mode control Hybrid couplings Mixed time-varying delays 

Notes

Acknowledgements

The authors would like to thank the Editors and the Reviewers for their insightful and constructive comments, which help to enrich the content and improve the presentation of the results in this paper. This work was jointly supported by the Natural Science Foundation of Hebei Province of China (A2018203288), High level talent support project of Hebei province of China (C2015003054) and the Postgraduate Innovation Project of Hebei province of China (CXZZSS2018048).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of ScienceYanshan UniversityQinhuangdaoChina

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