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Mathematical Problems in Engineering
Volume 2015, Article ID 314090, 12 pages
http://dx.doi.org/10.1155/2015/314090
Research Article

Sampled-Data Control of Nonlinear Systems with Quantization

School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China

Received 19 December 2014; Revised 6 April 2015; Accepted 6 April 2015

Academic Editor: Carsten Proppe

Copyright © 2015 Liu Cui and Dengping Duan. 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. T. W. Chen and B. Francis, Optimal Sampled-Data Control Systems, Springer, London, UK, 1995.
  2. P. Shi, “Filtering on sampled-data systems with parametric uncertainty,” IEEE Transactions on Automatic Control, vol. 43, no. 7, pp. 1022–1027, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. K. Abidi and J.-X. Xu, “Iterative learning control for sampled-data systems: from theory to practice,” IEEE Transactions on Industrial Electronics, vol. 58, no. 7, pp. 3002–3015, 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. T. Atsumi and W. C. Messner, “Analysis of unobservable oscillations in sampled-data positioning systems,” IEEE Transactions on Industrial Electronics, vol. 59, no. 10, pp. 3951–3960, 2012. View at Publisher · View at Google Scholar · View at Scopus
  5. H. Beikzadeh and H. J. Marquez, “Dissipativity of nonlinear multirate sampled-data systems under emulation design,” Automatica, vol. 49, no. 1, pp. 308–312, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. E. Fridman, A. Seuret, and J.-P. Richard, “Robust sampled-data stabilization of linear systems: an input delay approach,” Automatica, vol. 40, no. 8, pp. 1441–1446, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. H. Gao, J. Wu, and P. Shi, “Robust sampled-data H control with stochastic sampling,” Automatica, vol. 45, no. 7, pp. 1729–1736, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. H. J. Gao, W. C. Sun, and P. Shi, “Robust sampled-data H control for vehicle active suspension systems,” IEEE Transactions on Control Systems Technology, vol. 18, no. 1, pp. 238–245, 2010. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Hu, D. Yue, Z. Du, and J. Liu, “Reliable H non-uniform sampling tracking control for continuous-time non-linear systems with stochastic actuator faults,” IET Control Theory & Applications, vol. 6, no. 1, pp. 120–129, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. X. Yang, X. Cao, and H. Gao, “Sampled-data control for relative position holding of spacecraft rendezvous with thrust nonlinearity,” IEEE Transactions on Industrial Electronics, vol. 59, no. 2, pp. 1146–1153, 2012. View at Publisher · View at Google Scholar · View at Scopus
  11. B. Shen, Z. Wang, and X. H. Liu, “Sampled-data synchronization control of dynamical networks with stochastic sampling,” IEEE Transactions on Automatic Control, vol. 57, no. 10, pp. 2644–2650, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. H. Li, X. Jing, H. Lam, and P. Shi, “Fuzzy sampled-data control for uncertain vehicle suspension systems,” IEEE Transactions on Cybernetics, vol. 44, no. 7, pp. 1111–1126, 2014. View at Publisher · View at Google Scholar
  13. H. Shen, J. H. Park, L. Zhang, and Z.-G. Wu, “Robust extended dissipative control for sampled-data Markov jump systems,” International Journal of Control, vol. 87, no. 8, pp. 1549–1564, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. B. Shen, Z. Wang, and X. Liu, “A stochastic sampled-data approach to distributed H filtering in sensor networks,” IEEE Transactions on Circuits and Systems. I. Regular Papers, vol. 58, no. 9, pp. 2237–2246, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. M. Liu, J. You, and X. Ma, “H filtering for sampled-data stochastic systems with limited capacity channel,” Signal Processing, vol. 91, no. 8, pp. 1826–1837, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. E. Fridman, “A refined input delay approach to sampled-data control,” Automatica, vol. 46, no. 2, pp. 421–427, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. Z. Li, M. Liu, H. R. Karimi, and X. Cao, “Sampled-data control of spacecraft rendezvous with discontinuous Lyapunov approach,” Mathematical Problems in Engineering, vol. 2013, Article ID 814271, 10 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  18. W.-H. Chen, Z. P. Wang, and X. M. Lu, “On sampled-data control for master-slave synchronization of chaotic Lur'e systems,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 59, no. 8, pp. 515–519, 2012. View at Publisher · View at Google Scholar · View at Scopus
  19. Z. G. Wu, P. Shi, H. Su, and J. Chu, “Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 9, pp. 1368–1376, 2012. View at Publisher · View at Google Scholar · View at Scopus
  20. Z.-G. Wu, P. Shi, H. Y. Su, and J. Chu, “Sampled-data synchronization of chaotic Lur'e systems with time delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 3, pp. 410–421, 2013. View at Publisher · View at Google Scholar · View at Scopus
  21. H. K. Lam and W. K. Ling, “Sampled-data fuzzy controller for continuous nonlinear systems,” IET Control Theory and Applications, vol. 2, no. 1, pp. 32–39, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. H. K. Lam, “Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy-model-based control approach,” IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, vol. 42, no. 1, pp. 258–267, 2012. View at Publisher · View at Google Scholar · View at Scopus
  23. H. K. Lam and F. H. F. Leung, “Sampled-data fuzzy controller for time-delay nonlinear systems: fuzzy-model-based LMI approach,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 37, no. 3, pp. 617–629, 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. J. Yoneyama, “Robust H control of uncertain fuzzy systems under time-varying sampling,” Fuzzy Sets and Systems, vol. 161, no. 6, pp. 859–871, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. D. Yang and K.-Y. Cai, “Reliable H nonuniform sampling fuzzy control for nonlinear systems with time delay,” IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, vol. 38, no. 6, pp. 1606–1613, 2008. View at Publisher · View at Google Scholar · View at Scopus
  26. H. K. Lam and L. D. Seneviratne, “Chaotic synchronization using sampled-data fuzzy controller based on fuzzy-model-based approach,” IEEE Transactions on Circuits and Systems I, vol. 55, no. 3, pp. 883–892, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. X.-L. Zhu, B. Chen, D. Yue, and Y. Y. Wang, “An improved input delay approach to stabilization of fuzzy systems under variable sampling,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 2, pp. 330–341, 2012. View at Publisher · View at Google Scholar · View at Scopus
  28. Z.-G. Wu, P. Shi, H. Y. Su, and J. Chu, “Sampled-data fuzzy control of chaotic systems based on a T-S fuzzy model,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 1, pp. 153–163, 2014. View at Publisher · View at Google Scholar · View at Scopus
  29. Y.-Y. Cao and P. M. Frank, “Robust H disturbance attenuation for a class of uncertain discrete-time fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 8, no. 4, pp. 406–415, 2000. View at Publisher · View at Google Scholar · View at Scopus
  30. Y. H. Wang, Z. Y. Li, and S. Y. Zhang, “Approximation property of partition of unity and its applications,” Journal of Control Theory and Applications, vol. 2, no. 3, pp. 267–275, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  31. D. F. Han and Y. H. Wang, “State feedback H control for a class of nonlinear systems using partition of unity method,” International Journal of Control, Automation and Systems, vol. 7, no. 1, pp. 133–138, 2009. View at Publisher · View at Google Scholar · View at Scopus
  32. D. F. Han and Y. H. Wang, “Guaranteed cost control for a class of nonlinear time-delay systems based on partition of unity,” International Journal of Innovative Computing, Information and Control, vol. 4, no. 7, pp. 1685–1693, 2008. View at Google Scholar · View at Scopus
  33. D. F. Han and L. Shi, “Guaranteed cost control of affine nonlinear systems via partition of unity method,” Automatica, vol. 48, no. 2, pp. 660–666, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. E. J. Fuentes, C. A. Silva, and J. I. Yuz, “Predictive speed control of a two-mass system driven by a permanent magnet synchronous motor,” IEEE Transactions on Industrial Electronics, vol. 59, no. 7, pp. 2840–2848, 2012. View at Publisher · View at Google Scholar · View at Scopus
  35. R. K. Miller, A. N. Michel, and J. A. Farrell, “Quantizer effects on steady-state error specifications of digital feedback control systems,” IEEE Transactions on Automatic Control, vol. 34, no. 6, pp. 651–654, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  36. L. Hou, A. N. Michel, and H. Ye, “Some qualitative properties of sampled-data control systems,” IEEE Transactions on Automatic Control, vol. 42, no. 12, pp. 1721–1725, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  37. G. Guo, H. P. Xu, and T. Tian, “Sampled-data systems with quantization and slowly varying inputs,” in Intelligent Control and Automation, vol. 344 of Lecture Notes in Control and Information Sciences, pp. 584–589, Springer, 2006. View at Google Scholar
  38. D. W. Kim and H. J. Lee, “Stability connection between sampled-data fuzzy control systems with quantization and their approximate discrete-time model,” Automatica, vol. 45, no. 6, pp. 1518–1523, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  39. H. Ishii and B. A. Francis, “Quadratic stabilization of sampled-data systems with quantization,” Automatica, vol. 39, no. 10, pp. 1793–1800, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  40. 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 MathSciNet · View at Scopus
  41. H. J. Gao and T. W. Chen, “H estimation for uncertain systems with limited communication capacity,” IEEE Transactions on Automatic Control, vol. 52, no. 11, pp. 2070–2084, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  42. H. Zhang, J. Yang, and C.-Y. Su, “T-S fuzzy-model-based robust H design for networked control systems with uncertainties,” IEEE Transactions on Industrial Informatics, vol. 3, no. 4, pp. 289–301, 2007. View at Publisher · View at Google Scholar · View at Scopus