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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 471481, 14 pages
http://dx.doi.org/10.1155/2014/471481
Research Article

Stability of Infinite Dimensional Interconnected Systems with Impulsive and Stochastic Disturbances

1School of Transportation and Automotive Engineering, Xihua University, Chengdu 610039, China
2State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China

Received 29 March 2014; Revised 8 May 2014; Accepted 8 May 2014; Published 15 June 2014

Academic Editor: Hongli Dong

Copyright © 2014 Xiaohui Xu 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. X. Gong, Z.-C. Hou, C.-J. Zhao, Y. Bai, and Y.-T. Tian, “Adaptive backstepping sliding mode trajectory tracking control for a quad-rotor,” International Journal of Automation and Computing, vol. 9, no. 5, pp. 555–560, 2012. View at Publisher · View at Google Scholar · View at Scopus
  2. Y. Chen and K. A. Hoo, “Stability analysis for closed-loop management of a reservoir based on identification of reduced-order nonlinear model,” Systems Science and Control Engineering: An Open Access Journal, vol. 1, no. 1, pp. 12–19, 2013. View at Google Scholar
  3. H. Dong, Z. Wang, D. W. C. Ho, and H. Gao, “Robust H filtering for Markovian jump systems with randomly occurring nonlinearities and sensor saturation: the finite-horizon case,” IEEE Transactions on Signal Processing, vol. 59, no. 7, pp. 3048–3057, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  4. H. L. Dong, Z. D. Wang, and H. J. Gao, “Distributed filtering for a class of markovian jump nonlinear time-delay systems over lossy sensor networks,” IEEE Transaction on Industrial Electronics, vol. 60, no. 10, pp. 4665–4672, 2013. View at Google Scholar
  5. H. Dong, Z. Wang, and H. Gao, “Fault detection for Markovian jump systems with sensor saturations and randomly varying nonlinearities,” IEEE Transactions on Circuits and Systems: I: Regular Papers, vol. 59, no. 10, pp. 2354–2362, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  6. J.-G. Gao, F.-Q. Deng, C.-K. Zhang, and Y.-F. Sun, “Asymptotic stability of stochastic impulsive system via comparison approach,” in Proceedings of the 2nd International Asia Conference on Informatics in Control, Automation and Robotics (CAR '10), pp. 181–184, March 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. F. Yao and F. Deng, “Comparison principle and stability of impulsive stochastic functional differential systems in terms of two measures,” in Proceedings of the 8th IEEE International Conference on Control and Automation (ICCA '10), pp. 333–338, Xiamen, China, June 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. B. Liu, “Stability of solutions for stochastic impulsive systems via comparison approach,” IEEE Transactions on Automatic Control, vol. 53, no. 9, pp. 2128–2133, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  9. C. Li, J. Sun, and R. Sun, “Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 347, no. 7, pp. 1186–1198, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. Yang, S. Zhong, and W. Luo, “Mean square stability analysis of impulsive stochastic differential equations with delays,” Journal of Computational and Applied Mathematics, vol. 216, no. 2, pp. 474–483, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. L. Pan and J. Cao, “Exponential stability of impulsive stochastic functional differential equations,” Journal of Mathematical Analysis and Applications, vol. 382, no. 2, pp. 672–685, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J.-Z. Shi and J.-Y. Zhang, “String stability of infinite-dimension stochastic interconnected large-scale systems with time-varying delay,” International Journal of Systems Science: Principles and Applications of Systems and Integration, vol. 45, no. 5, pp. 1035–1041, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. X. H. Xu, J. Y. Zhang, and L. Tang, “String exponential stability with mode constraint of stochastic vehicle following systems,” ASME Journal of Dynamic Systems, Measurement, and Control, vol. 135, no. 6, Article ID 061011, 2013. View at Google Scholar
  14. J. Z. Shi, J. Y. Zhang, and J. Y. Tang, “The global exponential stability of a class of linear stochastic interconnected large-scale systems,” in Proceedings of the International Conference on Computer and Computational Intelligence, pp. 486–489, Nanning, Guangxi, China, 2010.
  15. J. Zhou and H. Peng, “Range policy of adaptive cruise control vehicles for improved flow stability and string stability,” IEEE Transactions on Intelligent Transportation Systems, vol. 6, no. 2, pp. 229–237, 2005. View at Publisher · View at Google Scholar · View at Scopus
  16. A. C. Schultz and L. E. Parker, Multi-Robot Systems: From Swarms to Intelligent AuTomata, Kluwer Academic, Dordrecht, The Netherlands, 2002.
  17. A. Pant, P. Seiler, and K. Hedrick, “Mesh stability of look-ahead interconnected systems,” IEEE Transactions on Automatic Control, vol. 47, no. 2, pp. 403–407, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  18. J. Zhang, Y. Suda, T. Iwasa, and H. Komine, “Vector Liapunov function approach to longitudinal control of vehicles in a platoon,” JSME International Journal C: Mechanical Systems, Machine Elements and Manufacturing, vol. 47, no. 2, pp. 653–658, 2004. View at Publisher · View at Google Scholar · View at Scopus
  19. L. Socha, “Stochastic stability of interconnected string systems,” Chaos, Solitons and Fractals, vol. 19, no. 4, pp. 949–955, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. J. Zhou, J. Lu, and H. Peng, “Vehicle stabilization in response to exogenous impulsive disturbances to the vehicle body,” in Proceedings of the American Control Conference (ACC '09), pp. 701–706, St. Louis, Mo, USA, June 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. J. Aracil, G. Heredia, and A. Ollero, “Global stability analysis of fuzzy path tracking using frequency response,” Engineering Applications of Artificial Intelligence, vol. 13, no. 2, pp. 109–119, 2000. View at Publisher · View at Google Scholar · View at Scopus
  22. D. Swaroop, J. Karl Hedrick, and S. B. Choi, “Direct adaptive longitudinal control of vehicle platoons,” IEEE Transactions on Vehicular Technology, vol. 50, no. 1, pp. 150–161, 2001. View at Publisher · View at Google Scholar · View at Scopus
  23. G. D. Lee and S. W. Kim, “A longitudinal control system for a platoon of vehicles using a fuzzy-sliding mode algorithm,” Mechatronics, vol. 12, no. 1, pp. 97–118, 2002. View at Publisher · View at Google Scholar · View at Scopus
  24. J. Z. Shi, J. Y. Zhang, and X. H. Xu, “String stability of stochastic interconnected systems with time delays,” Acta Automatica Sinica: Zidonghua Xuebao, vol. 36, no. 12, pp. 1744–1751, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. R. Z. Khasminski, Stochastic Stability of Differential Equations, vol. 7 of Monographs and Textbooks on Mechanics of Solids and Fluids: Mechanics and Analysis, Sijthoff & Noordhoff, Groningen, The Netherlands, 1980. View at MathSciNet
  26. Y. Niu and D. W. C. Ho, “Robust observer design for Itô stochastic time-delay systems via sliding mode control,” Systems & Control Letters, vol. 55, no. 10, pp. 781–793, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. D. J. Higham, “An algorithmic introduction to numerical simulation of stochastic differential equations,” SIAM Review, vol. 43, no. 3, pp. 525–546, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet