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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 718924, 12 pages
http://dx.doi.org/10.1155/2015/718924
Research Article

Quantized Feedback Control Design of Nonlinear Large-Scale Systems via Decentralized Adaptive Integral Sliding Mode Control

1School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, Jiangsu 210044, China
2CICAEET, School of Information and Control, Nanjing University of Information Science and Technology, Nanjing, Jiangsu 210044, China
3College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110819, China

Received 14 April 2015; Revised 19 June 2015; Accepted 12 July 2015

Academic Editor: Sarah K. Spurgeon

Copyright © 2015 Yan-Mei Xue et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. W. Brockett and D. Liberzon, “Quantized feedback stabilization of linear systems,” IEEE Transactions on Automatic Control, vol. 45, no. 7, pp. 1279–1289, 2000. View at Publisher · View at Google Scholar · View at Scopus
  2. D. Liberzon, “Hybrid feedback stabilization of systems with quantized signals,” Automatica, vol. 39, no. 9, pp. 1543–1554, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. T. Li and L. Xie, “Distributed coordination of multi-agent systems with quantized-observer based encoding-decoding,” IEEE Transactions on Automatic Control, vol. 57, no. 12, pp. 3023–3037, 2012. View at Publisher · View at Google Scholar · View at Scopus
  4. S. Hu and D. Yue, “Event-triggered control design of linear networked systems with quantizations,” ISA Transactions, vol. 51, no. 1, pp. 153–162, 2012. View at Publisher · View at Google Scholar · View at Scopus
  5. L. Li, Y. Xia, J. Qiu, and H. Yang, “Robust H networked control for discrete-time fuzzy systems with state quantisation,” International Journal of Systems Science, vol. 43, no. 12, pp. 2249–2260, 2012. View at Publisher · View at Google Scholar · View at Scopus
  6. L. Zhou and G. Lu, “Quantized feedback stabilization for networked control systems with nonlinear perturbation,” International Journal of Innovative Computing, Information and Control, vol. 6, no. 6, pp. 2485–2495, 2010. View at Google Scholar · View at Scopus
  7. W.-W. Che and G.-H. Yang, “H filter design for continuous-time systems with quantised signals,” International Journal of Systems Science, vol. 44, no. 2, pp. 265–274, 2013. View at Publisher · View at Google Scholar · View at Scopus
  8. M. L. Corradini and G. Orlando, “Robust quantized feedback stabilization of linear systems,” Automatica, vol. 44, no. 9, pp. 2458–2462, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. B.-C. Zheng, G.-H. Yang, and T. Li, “Quantised feedback sliding mode control of linear uncertain systems,” IET Control Theory & Applications, vol. 8, no. 7, pp. 479–487, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. L.-Y. Hao and G.-H. Yang, “Fault-tolerant control via sliding-mode output feedback for uncertain linear systems with quantisation,” IET Control Theory & Applications, vol. 7, no. 16, pp. 1992–2006, 2013. View at Publisher · View at Google Scholar · View at Scopus
  11. Y. Yan and X. Yu, “Quantization behaviors in equivalent-control based sliding-mode control systems,” in Advances in Sliding Mode Control, B. Bandyopad-hyay, S. Janardhanan, and S. Spurgeon, Eds., pp. 221–239, Springer, London, UK, 2013. View at Google Scholar
  12. M. Liu, X. Cao, S. Zhang, and W. Yang, “Sliding mode control of quantized systems against bounded disturbances,” Information Sciences, vol. 274, pp. 261–272, 2014. View at Publisher · View at Google Scholar · View at Scopus
  13. S. W. Yun, Y. J. Choi, and P. Park, “H2 control of continuous-time uncertain linear systems with input quantization and matched disturbances,” Automatica, vol. 45, no. 10, pp. 2435–2439, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. Y. Zou, Y. Niu, B. Chen, and T. Jia, “Networked predictive control of constrained linear systems with input quantisation,” International Journal of Systems Science, vol. 44, no. 10, pp. 1970–1982, 2013. View at Publisher · View at Google Scholar · View at Scopus
  15. J. Zhou, C. Wen, and G. Yang, “Adaptive backstepping stabilization of nonlinear uncertain systems with quantized input signal,” IEEE Transactions on Automatic Control, vol. 59, no. 2, pp. 460–464, 2014. View at Publisher · View at Google Scholar · View at Scopus
  16. M. Fu and L. Xie, “The sector bound approach to quantized feedback control,” IEEE Transactions on Automatic Control, vol. 50, no. 11, pp. 1698–1711, 2005. View at Publisher · View at Google Scholar · View at Scopus
  17. T. Kameneva and D. Nešić, “Robustness of quantized control systems with mismatch between coder/decoder initializations,” Automatica, vol. 45, no. 3, pp. 817–822, 2009. View at Publisher · View at Google Scholar · View at Scopus
  18. T. Kameneva and D. Nešić, “Robustness of nonlinear control systems with quantized feedback,” Nonlinear Analysis: Hybrid Systems, vol. 4, no. 2, pp. 306–318, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. C. D. Persis, “Robustness of quantized continuous-time nonlinear systems to encoder/decoder mismatch,” in Proceedings of the 48th IEEE Conference on Decision and Control, pp. 13–18, Shanghai, China, December 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. B.-C. Zheng and G.-H. Yang, “H2 control of linear uncertain systems considering input quantization with encoder/decoder mismatch,” ISA Transactions, vol. 52, no. 5, pp. 577–582, 2013. View at Publisher · View at Google Scholar · View at Scopus
  21. X.-G. Yan, J.-J. Wang, X.-Y. L{\"u}, and S.-Y. Zhang, “Decentralized output feedback robust stabilization for a class of nonlinear interconnected systems with similarity,” IEEE Transactions on Automatic Control, vol. 43, no. 2, pp. 294–299, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. X.-G. Yan, C. Edwards, and S. K. Spurgeon, “Decentralised robust sliding mode control for a class of nonlinear interconnected systems by static output feedback,” Automatica, vol. 40, no. 4, pp. 613–620, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. H.-T. Yau and J.-J. Yan, “Robust decentralized adaptive control for uncertain large-scale delayed systems with input nonlinearities,” Chaos, Solitons and Fractals, vol. 39, no. 4, pp. 1515–1521, 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. M. S. Mahmoud, A. Y. Al-Rayyah, and Y. Xia, “Quantised feedback stabilisation of interconnected discrete-delay systems,” IET Control Theory & Applications, vol. 5, no. 6, pp. 795–802, 2011. View at Publisher · View at Google Scholar · View at Scopus
  25. B.-C. Zheng and G.-H. Yang, “Decentralized sliding mode quantized feedback control for a class of uncertain large-scale systems with dead-zone input,” Nonlinear Dynamics, vol. 71, no. 3, pp. 417–427, 2013. View at Publisher · View at Google Scholar · View at Scopus
  26. L. Wu, X. Su, and P. Shi, “Sliding mode control with bounded 2 gain performance of Markovian jump singular time-delay systems,” Automatica, vol. 48, no. 8, pp. 1929–1933, 2012. View at Publisher · View at Google Scholar · View at Scopus
  27. I. R. Petersen, “A stabilization algorithm for a class of uncertain linear systems,” Systems & Control Letters, vol. 8, no. 4, pp. 351–357, 1987. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. F. Castaños, D. Hernández, and L. M. Fridman, “Integral sliding-mode control for linear time-invariant implicit systems,” Automatica, vol. 50, no. 3, pp. 971–975, 2014. View at Publisher · View at Google Scholar · View at Scopus
  29. Y. Niu, D. W. C. Ho, and J. Lam, “Robust integral sliding mode control for uncertain stochastic systems with time-varying delay,” Automatica, vol. 41, no. 5, pp. 873–880, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  30. C. Edwards and S. K. Spurgeon, Sliding Mode Control: Theory And Applications, Taylor & Francis, London, UK, 1998.
  31. V. I. Utkin, Sliding Modes in Control and Optimization, Communications and Control Engineering Series, Springer, Berlin, Germany, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  32. Q. Hu, G. Ma, and L. Xie, “Robust and adaptive variable structure output feedback control of uncertain systems with input nonlinearity,” Automatica, vol. 44, no. 2, pp. 552–559, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. F. H. Clarke, Y. S. Ledyaev, E. D. Sontag, and A. I. Subbotin, “Asymptotic controllability implies feedback stabilization,” IEEE Transactions on Automatic Control, vol. 42, no. 10, pp. 1394–1407, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. M. Krstić and P. V. Kokotović, “Control Lyapunov functions for adaptive non-linear stabilization,” Systems and Control Letters, vol. 26, no. 1, pp. 17–23, 1995. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  35. Y. S. Ledyaev and E. D. Sontag, “A Lyapunov characterization of robust stabilization,” Nonlinear Analysis: Theory, Methods & Applications, vol. 37, no. 7, pp. 813–840, 1999. View at Publisher · View at Google Scholar · View at MathSciNet