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Abstract and Applied Analysis
Volume 2014, Article ID 198616, 11 pages
http://dx.doi.org/10.1155/2014/198616
Research Article

Stochastic Finite-Time Performance Analysis of Continuous-Time Systems with Random Abrupt Changes

School of Information and Electrical Engineering, Panzhihua University, Panzhihua, Sichuan 617000, China

Received 10 December 2013; Accepted 21 January 2014; Published 3 March 2014

Academic Editor: Zhengguang Wu

Copyright © 2014 Bing Wang. 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. N. N. Krasovskiĭ and È. A. Lidskiĭ, “Analytical design of controllers in systems with random attributes,” Automation and Remote Control, vol. 22, pp. 1021–1025, 1961. View at Google Scholar · View at MathSciNet
  2. J. Cheng, H. Zhu, S. Zhong, and G. Li, “Novel delay-dependent robust stability criteria for neutral systems with mixed time-varying delays and nonlinear perturbations,” Applied Mathematics and Computation, vol. 219, no. 14, pp. 7741–7753, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  3. J. Cheng, H. Zhu, S. Zhong, Y. Zhang, and Y. Zeng, “Improved delay-dependent stability criteria for continuous system with two additive time-varying delay components,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 1, pp. 210–215, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  4. H. Shen, S. Xu, J. Lu, and J. Zhou, “Passivity-based control for uncertain stochastic jumping systems with mode-dependent round-trip time delays,” Journal of the Franklin Institute, vol. 349, no. 5, pp. 1665–1680, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. H. Shen, S. Xu, J. Zhou, and J. Lu, “Fuzzy H filtering for nonlinear Markovian jump neutral systems,” International Journal of Systems Science, vol. 42, no. 5, pp. 767–780, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. D. Zhang and L. Yu, “Exponential state estimation for Markovian jumping neural networks with time-varying discrete and distributed delays,” Neural Networks, vol. 35, pp. 103–111, 2012. View at Publisher · View at Google Scholar
  7. D. Zhang and L. Yu, “Passivity analysis for stochastic Markovian switching genetic regulatory networks with time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 8, pp. 2985–2992, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. D. Zhang, L. Yu, Q. Wang, and C. Ong, “Estimator Design for discrete-time switched neural networks with asynchronous switching and time-varying delay,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 5, pp. 827–834, 2012. View at Publisher · View at Google Scholar
  9. Z. Wu, P. Shi, H. Su, and J. Chu, “Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled-data,” IEEE Transactions on Cybernetics, vol. 43, no. 6, pp. 1796–1806, 2013. View at Google Scholar
  10. Z.-G. Wu, P. Shi, H. Su, and J. Chu, “Passivity analysis for discrete-time stochastic markovian jump neural networks with mixed time delays,” IEEE Transactions on Neural Networks, vol. 22, no. 10, pp. 1566–1575, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. H. Huang, G. Feng, and X. Chen, “Stability and stabilization of Markovian jump systems with time delay via new Lyapunov functionals,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 59, no. 10, pp. 2413–2421, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  12. H. Gao, Z. Fei, J. Lam, and B. Du, “Further results on exponential estimates of Markovian jump systems with mode-dependent time-varying delays,” IEEE Transactions on Automatic Control, vol. 56, no. 1, pp. 223–229, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  13. Z. Wu, P. Shi, H. Su, and J. Chu, “Asynchronous l2-l ltering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities,” Automatica, vol. 50, no. 1, pp. 180–186, 2014. View at Publisher · View at Google Scholar
  14. S. Hu, D. Yue, and J. Liu, “H filtering for networked systems with partly known distribution transmission delays,” Information Sciences. An International Journal, vol. 194, pp. 270–282, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. C.-H. Lien, “Robust observer-based control of systems with state perturbations via LMI approach,” IIEEE Transactions on Automatic Control, vol. 49, no. 8, pp. 1365–1370, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  16. 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
  17. Z. Wang, J. Lam, and X. Liu, “Exponential filtering for uncertain Markovian jump time-delay systems with nonlinear disturbances,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 51, no. 5, pp. 262–268, 2004. View at Publisher · View at Google Scholar · View at Scopus
  18. Y. Wang, C. Wang, and Z. Zuo, “Controller synthesis for Markovian jump systems with incomplete knowledge of transition probabilities and actuator saturation,” Journal of the Franklin Institute, vol. 348, no. 9, pp. 2417–2429, 2011. View at Publisher · View at Google Scholar · View at Scopus
  19. Q. Zhu, X. Yang, and H. Wang, “Stochastically asymptotic stability of delayed recurrent neural networks with both Markovian jump parameters and nonlinear disturbances,” Journal of the Franklin Institute, vol. 347, no. 8, pp. 1489–1510, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. O. M. Kwon, J. Park, S. Lee, and E. Cha, “Analysis on delay-dependent stability for neural networks with time-varying delays,” Neurocomputing, vol. 103, pp. 114–120, 2013. View at Publisher · View at Google Scholar
  21. F. Amato, R. Ambrosino, C. Cosentino, and G. De Tommasi, “Input-output finite time stabilization of linear systems,” Automatica, vol. 46, no. 9, pp. 1558–1562, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. J. Cheng, H. Zhu, S. Zhong, Y. Zeng, and X. Dong, “Finite-time H control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals,” ISA Transactions, vol. 52, pp. 768–774, 2013. View at Google Scholar
  23. J. Cheng, H. Zhu, S. Zhong, Y. Zhang, and Y. Li, “Finite-time H control for a class of discrete-time Markov jump systems with partly unknown time-varying transition probabilities subject to average dwell time switching,” International Journal of Systems Science, 2013. View at Publisher · View at Google Scholar
  24. J. Cheng, G. Li, H. Zhu, S. Zhong, and Y. Zeng, “Finite-time H control for a class of Markovian jump systems with mode-dependent time-varying delay,” Advances in Difference Equations, vol. 2013, article 214, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  25. S. He and F. Liu, “Stochastic finite-time boundedness of Markovian jumping neural network with uncertain transition probabilities,” Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems, vol. 35, no. 6, pp. 2631–2638, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. M. N. ElBsat and E. E. Yaz, “Robust and resilient finite-time bounded control of discrete-time uncertain nonlinear systems,” Automatica, vol. 49, no. 7, pp. 2292–2296, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  27. P. Park, J. W. Ko, and C. Jeong, “Reciprocally convex approach to stability of systems with time-varying delays,” Automatica, vol. 47, no. 1, pp. 235–238, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet