Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2015, Article ID 954782, 9 pages
http://dx.doi.org/10.1155/2015/954782
Research Article

Finite-Time Stabilization of Uncertain Switched Positive Linear Systems with Time-Varying Delays

1School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China
2School of Information Science and Engineering, Central South University, Changsha 410075, China

Received 30 September 2014; Revised 20 December 2014; Accepted 21 December 2014

Academic Editor: Muhammad Naveed Iqbal

Copyright © 2015 Tianjian Yu 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. D. Liberzon, Switching in Systems and Control, Springer, Boston, Mass, USA, 2003.
  2. Y. Zhong and T. Chen, “Robust observer design for switched positive linear system with uncertainties,” Abstract and Applied Analysis, vol. 2014, Article ID 745906, 9 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. A. Jadbabaie, J. Lin, and A. S. Morse, “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 988–1001, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. R. Shorten, F. Wirth, and D. Leith, “A positive systems model of TCP-like congestion control: asymptotic results,” IEEE/ACM Transactions on Networking, vol. 14, no. 3, pp. 616–629, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. E. Hernandez-Vargas, P. Colaneri, R. Middleton, and F. Blanchini, “Discrete-time control for switched positive systems with application to mitigating viral escape,” International Journal of Robust and Nonlinear Control, vol. 21, no. 10, pp. 1093–1111, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. Y. O. Lee, Y. S. Son, and C. C. Chung, “Clamping force control for an electric parking brake system: switched system approach,” IEEE Transactions on Vehicular Technology, vol. 62, no. 7, pp. 2937–2948, 2013. View at Publisher · View at Google Scholar · View at Scopus
  7. L. Gurvits, R. Shorten, and O. Mason, “On the stability of switched positive linear systems,” IEEE Transactions on Automatic Control, vol. 52, no. 6, pp. 1099–1103, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. X. Xue and Z. Li, “Asymptotic stability analysis of a kind of switched positive linear discrete systems,” IEEE Transactions on Automatic Control, vol. 55, no. 9, pp. 2198–2203, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. W. Xiang, J. Xiao, and I. M. Naveed, “Asymptotic stability, L2 gain boundness analysis and control synthesis for switched systems: a switching frequency approach,” International Journal of Adaptive Control and Signal Processing, vol. 26, no. 4, pp. 350–373, 2012. View at Google Scholar
  10. W. Xiang and J. Xiao, “Stability analysis and control synthesis of switched impulsive systems,” International Journal of Robust and Nonlinear Control, vol. 22, no. 13, pp. 1440–1459, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. X. Zhao, L. Zhang, P. Shi, and M. Liu, “Stability of switched positive linear systems with average dwell time switching,” Automatica, vol. 48, no. 6, pp. 1132–1137, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. X. Zhao, X. Liu, S. Yin, and H. Li, “Improved results on stability of continuous-time switched positive linear systems,” Automatica, vol. 50, no. 2, pp. 614–621, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. A. Benzaouia and F. Tadeo, “Stabilization of positive switching linear discrete-time systems,” International Journal of Innovative Computing, Information and Control, vol. 6, no. 6, pp. 2427–2437, 2010. View at Google Scholar · View at Scopus
  14. Y. Sun, “Stabilization of switched systems with nonlinear impulse effects and disturbances,” IEEE Transactions on Automatic Control, vol. 56, no. 11, pp. 2739–2743, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. W. Xiang and J. Xiao, “Stabilization of switched continuous-time systems with all modes unstable via dwell time switching,” Automatica, vol. 50, no. 3, pp. 940–945, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  16. X. Lin, S. Li, and Y. Zou, “Finite-time stability of switched linear systems with subsystems which are not finite-time stable,” IET Control Theory & Applications, vol. 8, no. 12, pp. 1137–1146, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  17. S. Mastellone, C. T. Abdallah, and P. Dorato, “Stability and finite time stability of discrete-time nonlinear networked control systems,” in Proceedings of the American Control Conference (ACC '05), pp. 1239–1244, June 2005. View at Scopus
  18. L. Wang, L. Cai, X. Liu, and X. Shen, “Practical stability and bounds of heterogeneous AIMD/RED system with time delay,” in Proceedings of the IEEE International Conference on Communications (ICC '08), pp. 5558–5563, May 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. X. Lin, H. Du, and S. Li, “Finite-time boundedness and L2 gain analysis for switched delay systems with norm-bounded disturbance,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5982–5993, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. M. Xiang and Z. Xiang, “Finite-time L1 control for positive switched linear systems with time-varying delay,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 11, pp. 3158–3166, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. H. Liu, Y. Shen, and X. Zhao, “Finite-time stabilization and boundedness of switched linear system under state-dependent switching,” Journal of the Franklin Institute, vol. 350, no. 3, pp. 541–555, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. Y. Zhong and T. Chen, “Finite-time boundedness analysis for a class of switched linear systems with time-varying delay,” Abstract and Applied Analysis, vol. 2014, Article ID 982414, 9 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. W. Xiang and J. Xiao, “H finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance,” Journal of the Franklin Institute, vol. 348, no. 2, pp. 331–352, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. X. Liu, D. W. C. Ho, W. Yu, and J. Cao, “A new switching design to finite-time stabilization of nonlinear systems with applications to neural networks,” Neural Networks, vol. 57, pp. 94–102, 2014. View at Publisher · View at Google Scholar · View at PubMed
  25. I. M. Naveed, J. Xiao, and W. Xiang, “Finite-time H-infinity sate estimation for discrete-time switched control systems under asynchronous switching,” Asian Journal of Control, vol. 16, no. 4, pp. 1112–1121, 2014. View at Google Scholar
  26. G. Chen and Y. Yang, “Finite-time stability of switched positive linear systems,” International Journal of Robust and Nonlinear Control, vol. 24, no. 1, pp. 179–190, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. G. Chen, Y. Yang, and Q. Pan, “Finite time stability analysis of switched systems with stable and unstable subsystems,” Asian Journal of Control, vol. 16, no. 4, pp. 1224–1228, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. J. Cheng, H. Zhu, S. Zhong, F. Zheng, and K. Shi, “Finite-time boundedness of a class of discrete-time Markovian jump systems with piecewise-constant transition probabilities subject to average dwell time switching,” Canadian Journal of Physics, vol. 92, no. 2, pp. 93–102, 2014. View at Publisher · View at Google Scholar · View at Scopus
  29. Y. Wang, X. Shi, G. Wang, and Z. Zuo, “Finite-time stability for continuous-time switched systems in the presence of impulse effects,” IET Control Theory & Applications, vol. 6, no. 11, pp. 1741–1744, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. L. Weiss and E. F. Infante, “Finite time stability under perturbing forces and on product spaces,” IEEE Transactions on Automatic Control, vol. 12, pp. 54–59, 1967. View at Google Scholar · View at MathSciNet
  31. P. Dorato, “An overview of finite-time stability,” in Current Trends in Nonlinear Systems and Control, pp. 185–194, Birkhauser, Boston, Mass, USA, 2006. View at Google Scholar
  32. B. Niu and J. Zhao, “Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems,” Systems and Control Letters, vol. 62, no. 10, pp. 963–971, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. N. Ben and J. Zhao, “P-times differentiable unbounded functions for roust control of uncertain nonlinear switched systems with tracking constraints,” International Journal of Robust and Nonlinear Control, 2014. View at Publisher · View at Google Scholar
  34. W. Xiang, J. Xiao, and M. N. Iqbal, “Robust observer design for nonlinear uncertain switched systems under asynchronous switching,” Nonlinear Analysis: Hybrid Systems, vol. 6, no. 1, pp. 754–773, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus