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Nonlinear Dynamics

, Volume 94, Issue 4, pp 2827–2839 | Cite as

Improved synchronization criteria of Lur’e systems under sampled-data control

  • Chao Ge
  • Bingfang Wang
  • Ju H. Park
  • Changchun Hua
Original Paper
  • 98 Downloads

Abstract

In this paper, we address the issue of \(\mathcal {H}_{\infty }\) synchronization for two identical chaotic systems with time-varying delays and uncertainties under sampled-data control. By developing some new terms, an improved piecewise Lyapunov–Krasovskii functional (LKF) is constructed to take full advantage of characteristic about real sampling and nonlinear function vector. Furthermore, some relaxed matrices constructed in LKF are not necessarily positive definite. By using the LKF and free-matrix-based integral inequality, some sufficient criteria can be obtained to ensure the stability of error systems and reduce the influence of external disturbances with an \(\mathcal {H}_{\infty }\) norm bound. The sampled-data controller can be synthesized by solving a group of linear matrix inequalities with the maximal sampling interval. Finally, the numerical examples are considered and analyzed by the proposed approach so as to show the benefit and the superiority of the proposed approach.

Keywords

Chaotic systems \(\mathcal {H}_{\infty }\) Sampled-data control Stability analysis 

Notes

Acknowledgements

This work of C. Ge was supported in part by the National Natural Science Foundation of China (Grant Number 61503120 ), in part by the Natural Science Foundation of Hebei Province (Grant Number F2016209382), in part by the Fostering Talents Foundation of North China University of Science and Technology (Grant Number JP201511), in part by the Excellent Going Abroad Experts’ Training Program in Hebei Province. Also, the work of J.H. Park was supported by Basic Science Research Programs through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant Number NRF-2017R1A2B2004671).

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.North China University of Science and TechnologyTangshanPeople’s Republic of China
  2. 2.Yeungnam UniversityKyongsanRepublic of Korea
  3. 3.Yanshan UniversityQinhuangdaoPeople’s Republic of China

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