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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 170794, 10 pages
http://dx.doi.org/10.1155/2014/170794
Research Article

Robust Control for a Class of Discrete Time-Delay Stochastic Systems with Randomly Occurring Nonlinearities

1Department of Mathematics, Yangzhou University, Yangzhou 225002, China
2Department of Basis Course, Lianyungang Technical College, Lianyungang 222006, China
3Communication Systems and Networks (CSN) Research Group, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
4Department of Computer Science, Brunel University, Uxbridge, Middlesex UB8 3PH, UK

Received 14 July 2014; Accepted 1 August 2014; Published 31 August 2014

Academic Editor: Hongli Dong

Copyright © 2014 Yamin Wang 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. E. K. Boukas and Z.-K. Liu, Deterministic and Stochastic Time-Delay Systems, Birkhauser, Boston, Mass, USA, 2002.
  2. S. Elmadssia, K. Saadaoui, and M. Benrejeb, “New delay-dependent stability conditions for linear systems with delay,” Systems Science and Control Engineering, vol. 1, no. 1, pp. 2–11, 2013. View at Publisher · View at Google Scholar
  3. J. Shen and J. Lam, “Decay rate constrained stability analysis for positive systems with discrete and distributed delays,” Systems Science and Control Engineering, vol. 2, no. 1, pp. 7–12, 2014. View at Publisher · View at Google Scholar
  4. M. Kermani and A. Sakly, “Stability analysis for a class of switched nonlinear time-delay systems,” Systems Science and Control Engineering: An Open Access Journal, vol. 2, no. 1, pp. 80–89, 2014. View at Google Scholar
  5. Z. Wang, D. W. C. Ho, and X. Liu, “A note on the robust stability of uncertain stochastic fuzzy systems with time-delays,” IEEE Transactions on Systems, Man, and Cybernetics A, vol. 34, no. 4, pp. 570–576, 2004. View at Publisher · View at Google Scholar · View at Scopus
  6. S. Xu and T. Chen, “Robust H control for uncertain stochastic systems with state delay,” IEEE Transactions on Automatic Control, vol. 47, no. 12, pp. 2089–2094, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. H. Gao, J. Lam, and C. Wang, “Robust energy-to-peak filter design for stochastic time-delay systems,” Systems and Control Letters, vol. 55, no. 2, pp. 101–111, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. 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 MathSciNet · View at Scopus
  9. H. Gao, C. Wang, and J. Wang, “On Hα performance analysis for continuous-time stochastic systems with polytopic uncertainties,” Circuits, Systems and Signal Processing, vol. 24, no. 4, pp. 415–429, 2005. View at Google Scholar
  10. H. K. Khalil, Nonlinear Systems, Prentice-Hall, Upper Saddle River, NJ, USA, 1996.
  11. Q.-L. Han, “Absolute stability of time-delay systems with sector-bounded nonlinearity,” Automatica, vol. 41, no. 12, pp. 2171–2176, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. S. J. Kim and I. J. Ha, “A state-space approach to analysis of almost periodic nonlinear systems with sector nonlinearities,” IEEE Transaction on Automatic Control, vol. 44, no. 1, pp. 66–70, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. J. Lam, H. Gao, S. Xu, and C. Wang, “H and L2=L model reduction for system input with sector nonlinearities,” Journal of Optimization Theory and Applications, vol. 125, no. 1, pp. 137–155, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. W. M. McEneaney, G. Yin, and Q. Zhang, Eds., Stochastic Analysis, Control, Optimization and Applications, Systems and Control: Foundations and Applications series, Birkhäuser, Boston, Mass, USA, 1999.
  15. C. D. Charalambous, “Stochastic nonlinear minimax dynamic games with noisy measurements,” IEEE Transactions on Automatic Control, vol. 48, no. 2, pp. 261–266, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. H. Deng and M. Krstić, “Output-feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance,” Systems & Control Letters, vol. 39, no. 3, pp. 173–182, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. H. Deng, M. Krstic, and R. J. Williams, “Stabilization of stochastic nonlinear systems driven by noise of unknown covariance,” IEEE Transactions on Automatic Control, vol. 46, no. 8, pp. 1237–1253, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. Y. Liu, Z. Pan, and S. Shi, “Output feedback control design for strict-feedback stochastic nonlinear systems under a risk-sensitive cost,” IEEE Transactions on Automatic Control, vol. 48, no. 3, pp. 509–513, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. S. Xie and L. Xie, “Decentralized stabilization of a class of interconnected stochastic nonlinear systems,” IEEE Transactions on Automatic Control, vol. 45, no. 1, pp. 132–137, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. N. Berman and U. Shaked, “H control for discrete-time nonlinear stochastic systems,” IEEE Transactions on Automatic Control, vol. 51, no. 6, pp. 1041–1046, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. H. Shu and G. Wei, “H analysis of nonlinear stochastic time-delay systems,” Chaos, Solitons and Fractals, vol. 26, no. 2, pp. 637–647, 2005. View at Publisher · View at Google Scholar · View at Scopus
  22. W. Zhang, B. Chen, and C. Tseng, “Robust H filtering for nonlinear stochastic systems,” IEEE Transactions on Signal Processing, vol. 53, no. 2, part 1, pp. 589–598, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. A. J. Shaiju and I. R. Petersen, “Discrete-time robust H control of a class of nonlinear uncertain systems,” International Journal of Robust and Nonlinear Control, vol. 23, no. 14, pp. 1629–1641, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. S. Zhang, Z. Wang, and D. Ding, “H fuzzy control with randomly occurring infinite distributed delays and channel fadings,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 1, pp. 189–200, 2014. View at Google Scholar
  25. X. Chang and G. Yang, “New results on output feedback H control for linear discrete-time systems,” IEEE Transactions on Automatic Control, vol. 59, no. 5, pp. 1355–1359, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  26. Z. Wang, D. Ding, H. Dong, and H. Shu, “H consensus control for multi-agent systems with missing measurements: the finite-horizon case,” Systems and Control Letters, vol. 62, no. 10, pp. 827–836, 2013. View at Publisher · View at Google Scholar · View at Scopus
  27. L. Wang, G. Wei, and W. Li, “Probability-dependent H synchronization control for dynamical networks with randomly varying nonlinearities,” Neurocomputing, vol. 133, pp. 369–376, 2014. View at Publisher · View at Google Scholar
  28. H. Dong, Z. Wang, and H. Gao, “Distributed H∞ filtering for a class of markovian jump nonlinear time-delay systems over lossy sensor networks,” IEEE Transactions on Industrial Electronics, vol. 60, no. 10, pp. 4665–4672, 2013. View at Publisher · View at Google Scholar · View at Scopus
  29. H. Gao, J. Lam, L. Xie, and C. Wang, “New approach to mixed H2=H filtering for polytopic discrete-time systems,” IEEE Transactions on Signal Processing, vol. 53, no. 8, part 2, pp. 3183–3192, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus