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Asymptotic Stability of Master-slave Systems Using Sampled-data Controller with Time-delay

  • Regular Papers
  • Control Theory and Applications
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Abstract

In this paper, the synchronization of Chaotic Lur’e systems subject to aperiodic sampling is investigated. It is shown that sampling interval is bounded and nonuniform. A modified free-matrix-based (MFMB) time-dependent Lyapunov functional is developed to capture the information on sampling pattern, which is sufficiently used to analyze stability of Chaotic Lur’e systems. For a special case that the sampled-data controller suffers constant input delay, a discontinuous Lyapunov functional is presented based on the vector extension of Wirtinger’s inequality. The obtained stability condition leads to a less computational complexity than some of existing works. A longer value on the calculation of sampling interval is achieved. Two illustrative examples demonstrate the effectiveness of designed methods and less conservatism of the obtained results.

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References

  1. T. L. Carrol and L. M. Pecora, “Synchronizing chaotic systems,” IEEE Trans. on Circuits System. I, Fundam. Theory Appl, vol. 38, no. 4, pp. 445–456, April 1991.

    Google Scholar 

  2. H. R. Karimi, “A sliding mode approach to H ∞ synchronization of master-slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties,” Journal of the Franklin Institute, vol. 349, no. 4, pp. 1480–1496, May 2012.

    Article  MathSciNet  MATH  Google Scholar 

  3. H. R. Karimi, “Robust delay-dependent H ∞ control of uncertain time-delay systems with mixed neutral, discrete, and distributed time-delays and markovian switching parameters,” IEEE Trans. on Circuits & Systems I: Regular Papers, vol. 58, no. 8, pp. 1910–1923, 2011.

  4. H. R. Karimi, “Robust synchronization and fault detection of uncertain master-slave systems with mixed time-varying delays and nonlinear perturbations,” International Journal of Control Automation & Systems, vol. 9, no. 4, pp. 671–680, 2011.

    Article  Google Scholar 

  5. K. B. Shi, Y. Y. Tang, X. Z. Liu, and S. M. Zhong, “Non-fragile sampled-data robust synchronization of uncertain delayed chaotic Lur’e systems with randomly occurring controller gain fluctuation,” Isa Transactions, vol. 66, pp. 185–199, January 2017.

    Article  Google Scholar 

  6. K. B. Shi, Y. Y. Tang, S. M. Zhong, C. Yin, X. G. Huang, and W. Q. Wang, “Nonfragile asynchronous control for uncertain chaotic Lurie network systems with Bernoulli stochastic process,” Isa Transactions, vol. 28, no. 44 pp. 1693–1714, November 2017.

    MathSciNet  MATH  Google Scholar 

  7. X. Z. Jin, G. H. Yang, and W. W. Che, “Adaptive synchronization of master-slave large-scale systems against bias actuators and network attenuations,” International Journal of Control Automation & Systems, vol. 10, no. 6, pp. 1102–1110, December 2012.

    Article  Google Scholar 

  8. S. Song, X. N. Song, N. Pathak, and I. T. Balsera, “Multiswitching adaptive synchronization of two fractional-order chaotic systems with different structure and different order,” International Journal of Control Automation & Systems, vol. 15, no. 4, pp. 1524–1535, June 2017.

    Article  Google Scholar 

  9. R. Lu, P. Shi, H. Su, Z.-G. Wu, and J. Lu, “Synchronization of general chaotic neural networks with nonuniform sampling and packet missing: a switched system approach,” IEEE Trans. on Neural Networks and Learning Systems, vol. 29, no. 3 pp.523–533, March 2018.

    Article  MathSciNet  Google Scholar 

  10. J. G. Lu and D. J. Hill, “Global asymptotical synchronization of chaotic Lur’e systems using sampled data: A linear matrix inequality approach,” IEEE Trans. on Circuits & Systems II: Express Briefs, vol. 55, no. 6, pp. 586–590, 2008.

    Article  Google Scholar 

  11. K. B. Shi, X. Z. Liu, H. Zhu, Y. Zeng, and C. Yin, “Novel delay-dependent master-slave synchronization criteria of chaotic Lur’e systems with time-varying-delay feedback control,” Applied Mathematics & Computation, vol. 282, pp. 137–154, May 2016.

    Article  MathSciNet  MATH  Google Scholar 

  12. Z. G. Wu, P. Shi, H. Su, and J. Chu, “Sampled-data fuzzy control of chaotic systems based on a T-S fuzzy model,” IEEE Trans. on Fuzzy Systems, vol. 22, no. 1, pp. 153–163, February 2014.

    Article  Google Scholar 

  13. W. H. Chen and W. X. Zheng, “An improved stabilization method for sampled-Data control systems with control packet loss,” IEEE Trans. on Automatic Control, vol. 57, no. 9, pp. 2378–2384, September 2012.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. H. Kim, C. H. Chang, E. Kim, and M. Park, “Adaptive synchronization of uncertain chaotic systems based on T-S fuzzy model,” IEEE Trans. on Fuzzy Systems, vol. 15, no. 3, pp. 359–369, July 2007.

    Article  Google Scholar 

  15. G. P. Jiang, W. X. Zheng, K. S. Tang, and G. R. Chen, “Integral-observer-based chaos synchronization,” IEEE Trans. on Circuits & Systems II: Express Briefs, vol. 53, no. 2, pp. 110–114, February 2006.

    Article  Google Scholar 

  16. S. Mohammadpour and T. Binazadeh, “Observer-based synchronization of uncertain chaotic systems subject to input saturation,” Transactions of the Institute of Measurement & Control, vol. 40, no. 8, pp. 2526–2535, 2018.

    Article  Google Scholar 

  17. Y. Q. Wu, H. Y. Su, P. Shi, Z. Shu, and Z. G. Wu, “Consensus of multiagent systems using aperiodic sampled-data control,” IEEE Trans. Cybernetics, vol. 46, no. 9, pp. 2132–2143, August 2015.

    Article  Google Scholar 

  18. Y. Q. Wu, R. Q. Lu, P. Shi, H. Y. Su, and Z. G. Wu, “Sampled-data synchronization of complex networks with partial couplings and T-S fuzzy nodes,” IEEE Trans. Fuzzy Systems, vol. 26, no. 2, pp. 782–793, March 2017.

    Article  Google Scholar 

  19. E. Fridman, “Introduction to time-delay and sampled-data systems,” European Control Conference, pp. 1428–1433, June 2014.

    Google Scholar 

  20. H. B. Zeng, Y. He, M. Wu, and S. P. Xiao, “Less conservative results on stability for linear systems with a time-varying delay,” Optimal Control Applications & Methods, vol. 34, no. 6, pp. 670–679, November 2013.

    Article  MathSciNet  MATH  Google Scholar 

  21. X. M. Zhang, M. Wu, J. H. She, and Y. He, “Delay-dependent stabilization of linear systems with time-varying state and input delays,” Optimal Control Applications & Methods, vol. 41, no. 8, pp. 1405–1412, August 2005.

    MathSciNet  MATH  Google Scholar 

  22. M. Wu, Y. He, J. H. She, and G. P. Liu, “Delay-dependent criteria for robust stability of time-varying delay systems,” Automatica, vol. 40, no. 8, pp. 1435–1439, August 2004.

    Article  MathSciNet  MATH  Google Scholar 

  23. K. Liu and E. Fridman, “Wirtinger’s inequality and Lyapunov-based sampled-data stabilization,” Automatica, vol. 48, no. 1, pp. 102–108, January 2012.

    Article  MathSciNet  MATH  Google Scholar 

  24. D. Y. Yao, B. Zhang, P. S. Li, and H. Y. Li, “Event-triggered sliding mode control of discrete-time Markov jump systems,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2018. DOI: https://doi.org/10.1109/TSMC.2018.2836390

    Google Scholar 

  25. H. B. Zeng, Y. He, M. Wu, and J. H. She, “Free-matrix-based integral inequality for stability analysis of systems with time-varying delay,” IEEE Trans. on Automatic Control, vol. 60, no. 10, pp. 2768–2772, October 2015.

    Article  MathSciNet  MATH  Google Scholar 

  26. R. M. Zhang, D. Q Zeng, and S. M. Zhong, “Novel master-slave synchronization criteria of chaotic Lur’e systems with time delays using sampled-data control,” Journal of the Franklin Institute, vol. 354, no. 12, pp. 4930–4954, May 2017.

    Article  MathSciNet  MATH  Google Scholar 

  27. X. C. Shang-Guan, Y. He, W. J. Lin, and M. Wu, “Improved synchronization of chaotic Lur’e systems with time delay using sampled-data control,” Journal of the Franklin Institute, vol. 354, no. 3, pp. 1618–1636, January 2016.

    Article  MathSciNet  MATH  Google Scholar 

  28. R. E. Skelton, T. Iwasaki, and M. Karolos, A Unified Algebraic Approach to Control Design, Taylor & Francis, CRC Press, 1997.

    Google Scholar 

  29. T. H. Lee and H. P. Ju, “Stability analysis of sampled-data systems via free-matrix-based time-dependent discontinuous lyapunov approach,” IEEE Trans. on Automatic Control, vol. 62, no. 7, pp. 3653–3657, February 2017.

    Article  MathSciNet  MATH  Google Scholar 

  30. K. Liu, V. Suplin, and E. Fridman, “Stability of linear systems with general sawtooth delay,” Journal of Mathematical Control & Information, vol. 27, no. 4, pp. 419–436, December 2010.

    Article  MathSciNet  MATH  Google Scholar 

  31. C. Hua, C. Ge, and X. Guan, “Synchronization of chaotic Lur’e systems with time delays using sampled-data,” IEEE Trans. on Neural Network and Learning System, vol. 26, no. 6, pp. 1214–1221, July 2014.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Automation, and the Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou, 510006, Guangdong, China

    Shenghuang He, Yuanqing Wu & Yanzhou Li

Authors
  1. Shenghuang He
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  2. Yuanqing Wu
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  3. Yanzhou Li
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Corresponding author

Correspondence to Yuanqing Wu.

Additional information

Recommended by Associate Editor Muhammad Rehan under the direction of Editor Fuchun Sun. This work was supported by the China National Funds for Distinguished Young Scientists under Grant (61425009), the National Natural Science Foundation of China under Grants (U1611262,61603102), Guangdong Province Higher Vocational Colleges & Schools Pearl River Scholar approved in 2018, the Guangdong Natural Science Funds for Distinguished Young Scholar (2018B030306013), the Innovative Research Team Program of Guangdong Province Science Foundation (2018B030312006), and the Science and Technology Planning Project of Guangdong Province (2017B010116006).

Shenghuang He was born in 1992. He received his B.Eng. degree from the Guangdong University of Petrochemical Technology, Maoming, China, in 2015. He is currently pursuing a Ph.D. degree in the School of Automation, Guangdong University of Technology, Guangzhou, China. His current research interests include robust control, multiagent systems, and sampled-data control.

Yuanqing Wu received his Ph.D. degree in the Department of Control Science and Engineering, Zhejiang University, Hangzhou, China, in 2016. Now, he is working in Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou. His current research interests include robust control, multiagent systems, output regulation theory, sampled-data control, and event-trigger control.

Yanzhou Li was born in 1992. He received the B.Eng. degree from the Henan Institute of Science and Technology, Xinxiang, China, in 2015. He is currently pursuing a master’s degree in control science and control engineering with the Guangdong University of Technology, Guangzhou, China. His current research interests include robust control, network systems, and sampled-data control

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He, S., Wu, Y. & Li, Y. Asymptotic Stability of Master-slave Systems Using Sampled-data Controller with Time-delay. Int. J. Control Autom. Syst. 17, 1473–1482 (2019). https://doi.org/10.1007/s12555-018-0264-x

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  • DOI: https://doi.org/10.1007/s12555-018-0264-x

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