Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 931695, 9 pages
http://dx.doi.org/10.1155/2013/931695
Research Article

Full-State Linearization and Stabilization of SISO Markovian Jump Nonlinear Systems

State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China

Received 18 January 2013; Revised 13 March 2013; Accepted 18 March 2013

Academic Editor: Rongni Yang

Copyright © 2013 Zhongwei Lin 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. M. M. Mahmoud, J. Jiang, and Y. Zhang, Active Fault Tolerant Control Systems, vol. 287 of Lecture Notes in Control and Information Sciences, Springer, New York, NY, USA, 2003. View at Zentralblatt MATH · View at MathSciNet
  2. M. Mariton, Jump Linear Systems in Automatic Control, Marcel Dekker, New York, NY, USA, 1990.
  3. R. C. Tsaur, “A fuzzy time series-Markov chain model with an application to forecast the exchange rate between the Taiwan and US dollar,” International Journal of Innovative Computing, Information and Control, vol. 8, no. 7, pp. 4931–4942, 2012. View at Google Scholar
  4. F. Kojima and J. S. Knopp, “Inverse problem for electromagnetic propagation in a dielectric medium using Markov chainMonte Carlo method,” International Journal of Innovative Computing, Information and Control, vol. 8, no. 3, pp. 2339–2346, 2012. View at Google Scholar
  5. Q. Ahmed, A. Iqbal, I. Taj, and K. Ahmed, “Gasoline engine intake manifold leakage diagnosis/prognosis using hidden Markov model,” International Journal of Innovative Computing, Information and Control, vol. 8, no. 7, pp. 4661–4674, 2012. View at Google Scholar
  6. P. Shi, E.-K. Boukas, and R. K. Agarwal, “Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters,” IEEE Transactions on Automatic Control, vol. 44, no. 8, pp. 1592–1597, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. P. Shi, E.-K. Boukas, and R. K. Agarwal, “Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay,” IEEE Transactions on Automatic Control, vol. 44, no. 11, pp. 2139–2144, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Z. Wang, H. Qiao, and K. J. Burnham, “On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters,” IEEE Transactions on Automatic Control, vol. 47, no. 4, pp. 640–646, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. Lam, Z. Shu, S. Xu, and E.-K. Boukas, “Robust H control of descriptor discrete-time Markovian jump systems,” International Journal of Control, vol. 80, no. 3, pp. 374–385, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. L. Wu, X. Su, and P. Shi, “Sliding mode control with bounded L2 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 MathSciNet
  11. L. Wu, P. Shi, and H. Gao, “State estimation and sliding-mode control of Markovian jump singular systems,” IEEE Transactions on Automatic Control, vol. 55, no. 5, pp. 1213–1219, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  12. X. Su, P. Shi, L. Wu, and Y. Song, “A novel approach to filter design for T-S fuzzy discrete-time systems with time-varying delay,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 6, pp. 1114–1129, 2012. View at Google Scholar
  13. R. Yang, H. Gao, and P. Shi, “Novel robust stability criteria for stochastic Hopfield neural networks with time delays,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 39, no. 2, pp. 467–474, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. R. Yang, P. Shi, G.-P. Liu, and H. Gao, “Network-based feedback control for systems with mixed delays based on quantization and dropout compensation,” Automatica, vol. 47, no. 12, pp. 2805–2809, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. Z. Fei, H. Gao, and P. Shi, “New results on stabilization of Markovian jump systems with time delay,” Automatica, vol. 45, no. 10, pp. 2300–2306, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. X. Mao and C. Yuan, Stochastic differential equations with Markovian switching, Imperial College Press, London, UK, 2006. View at MathSciNet
  17. M. D. S. Aliyu, “Passivity and stability of nonlinear systems with Markovian jump parameters,” in Proceedings of the American Control Conference (ACC '99), pp. 953–957, June 1999. View at Scopus
  18. Z. W. Lin, Y. Lin, and W. H. Zhang, “A unified design for state and output feedback H control of nonlinear stochastic Markovian jump systems with state and disturbance-dependent noise,” Automatica, vol. 45, no. 12, pp. 2955–2962, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. Z. W. Lin, J. Z. Liu, W. H. Zhang, and Y. G. Niu, “Stabilization of interconnected nonlinear stochastic Markovian jump systems via dissipativity approach,” Automatica, vol. 47, no. 12, pp. 2796–2800, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. Z.-J. Wu, X.-J. Xie, P. Shi, and Y.-Q. Xia, “Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching,” Automatica, vol. 45, no. 4, pp. 997–1004, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. J. C. Willems, “Dissipative dynamical systems. I. General theory,” Archive for Rational Mechanics and Analysis, vol. 45, pp. 321–393, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. D. J. Hill and P. J. Moylan, “The stability of nonlinear dissipative systems,” IEEE Transactions on Automatic Control, vol. 21, no. 5, pp. 708–711, 1976. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. C. I. Byrnes, A. Isidori, and J. C. Willems, “Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems,” IEEE Transactions on Automatic Control, vol. 36, no. 11, pp. 1228–1240, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. W. Lin and T. Shen, “Robust passivity and feedback design for minimum-phase nonlinear systems with structural uncertainty,” Automatica, vol. 35, no. 1, pp. 35–47, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. A. Isidori, Nonlinear Control System, Springer, Berlin, Germany, 1994.
  26. H. K. Khalil, Nonlinear Systems, Prentice Hall, New York, NY, USA, 2002.