About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 905968, 10 pages
http://dx.doi.org/10.1155/2014/905968
Research Article

Discretized Lyapunov Function Approach for Switched Linear Systems under Dwell Time Constraint

1School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China
2Institute of Information Security and Computing Technology, Mianyang Normal University, Mianyang 621006, China
3School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 610031, China

Received 14 March 2014; Accepted 18 June 2014; Published 3 July 2014

Academic Editor: Jaeyoung Chung

Copyright © 2014 Yongchi Zhao 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 Cystems and Control, Birkhäuser, Boston, Mass, USA, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  2. Z. Sun and S. Ge, Switched Linear Systems-Control and Design, Springer, London, UK, 2005.
  3. R. A. Decarlo, M. S. Branicky, S. Pettersson, and B. Lennartson, “Perspectives and results on the stability and stabilizability of hybrid systems,” Proceedings of the IEEE, vol. 88, no. 7, pp. 1069–1082, 2000. View at Publisher · View at Google Scholar · View at Scopus
  4. H. Lin and P. J. Antsaklis, “Stability and stabilizability of switched linear systems: a survey of recent results,” IEEE Transactions on Automatic Control, vol. 54, no. 2, pp. 308–322, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. A. Balluchi, M. D. Benedetto, C. Pinello, C. Ross, and A. Sangiovanni-Vincentelli, “Cut-off in engine control: a hybrid system approach,” in Proceedings of the 36th IEEE Conference on Decision and Control, pp. 4720–4725, San Diego, Calif, USA, December 1997. View at Scopus
  6. B. E. Bishop and M. W. Spong, “Control of redundant manipulators using logic-based switching,” in Proceedings of the 37th IEEE Conference on Decision and Control (CDC '98), pp. 1488–1493, Tampa, Fla, USA, December 1998. View at Scopus
  7. W. Zhang, M. S. Branicky, and S. M. Phillips, “Stability of networked control systems,” IEEE Control Systems Magazine, vol. 21, no. 1, pp. 84–99, 2001. View at Publisher · View at Google Scholar · View at Scopus
  8. I. Kolmanovsky and S. Jing, “A multi-mode switching-based command tracking in network controlled systems with pointwise-in-time constraints and disturbance inputs,” in Proceedings of the 6th World Congress on Intelligent Control and Automation (WCICA '06), pp. 199–204, Dalian, China, June 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. K. S. Narendra, O. A. Driollet, M. Feiler, and K. George, “Adaptive control using multiple models, switching and tuning,” International Journal of Adaptive Control and Signal Processing, vol. 17, no. 2, pp. 87–102, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. B. Castillo-Toledo, S. Di Gennaro, A. G. Loukianov, and J. Rivera, “Hybrid control of induction motors via sampled closed representations,” IEEE Transactions on Industrial Electronics, vol. 55, no. 10, pp. 3758–3771, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. C. Sreekumar and V. Agarwal, “A hybrid control algorithm for voltage regulation in DC-DC boost converter,” IEEE Transactions on Industrial Electronics, vol. 55, no. 6, pp. 2530–2538, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. R. Shorten, F. Wirth, O. Mason, K. Wulff, and C. King, “Stability criteria for switched and hybrid systems,” SIAM Review, vol. 49, no. 4, pp. 545–592, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. M. S. Branicky, “Multiple Lyapunov functions and other analysis tools for switched and hybrid systems,” IEEE Transactions on Automatic Control, vol. 43, no. 4, pp. 475–482, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. K. S. Narendra and J. A. Balakrishnan, “A common Lyapunov function for stable LTI systems with commuting A-matrices,” IEEE Transactions on Automatic Control, vol. 39, no. 12, pp. 2469–2471, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. J. Daafouz, P. Riedinger, and C. Iung, “Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach,” IEEE Transactions on Automatic Control, vol. 47, no. 11, pp. 1883–1887, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. 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
  17. L. I. Allerhand and U. Shaked, “Robust stability and stabilization of linear switched systems with dwell time,” IEEE Transactions on Automatic Control, vol. 56, no. 2, pp. 381–386, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. J. C. Geromel and P. Colaneri, “Stability and stabilization of discrete time switched systems,” International Journal of Control, vol. 79, no. 7, pp. 719–728, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  19. K. Hirata and J. P. Hespanha, “2-induced gain analysis for a class of switched systems,” in Proceeding of thr 48th IEEE Conference on Decision and Control held jointly with the 28th Chinese Control Conference (CDC/CCC '09), pp. 2138–2143, Shanghai, China, December 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. K. Hirata and J. Hespanha, “L2-induced gain analysis of switched linear systems via finitely parametrized storage functions,” in Proceedings of the 29th American Control Conference (ACC '10), pp. 4064–4069, Baltimore, Md, USA, June 2010.
  21. 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
  22. W. Xiang, J. Xiao, and M. N. Iqbal, “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 Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. M. Margaliot and J. P. Hespanha, “Root-mean-square gains of switched linear systems: a variational approach,” Automatica, vol. 44, no. 9, pp. 2398–2402, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. A. S. Morse, “Supervisory control of families of linear set-point controllers. I. Exact matching,” IEEE Transactions on Automatic Control, vol. 41, no. 10, pp. 1413–1431, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. J. P. Hespanha and A. S. Morse, “Stability of switched systems with average dwell-time,” in Proceedings of the 38th IEEE Conference on Decision and Control (CDC '99), pp. 2655–2660, Phoenix, Ariz, USA, December 1999. View at Scopus
  26. L. Zhang and P. Shi, “Stability, l2-gain and asynchronous H control of discrete-time switched systems with average dwell time,” IEEE Transactions on Automatic Control, vol. 54, no. 9, pp. 2192–2199, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. J. Hespanha, “L2-induced gains of switched linear systems,” in Unsolved Problems in Mathematical Systems and Control Theory, V. D. Blondel and A. Megretski, Eds., pp. 131–133, Princeton University Press, Princeton, NJ, USA, 2003.
  28. G. Zhai, B. Hu, K. Yasuda, and A. N. Michel, “Disturbance attenuation properties of time-controlled switched systems,” Journal of the Franklin Institute, vol. 338, no. 7, pp. 765–779, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. G. Zhai, B. Hu, K. Yasuda, and A. N. Michel, “Qualitative analysis of discrete-time switched systems,” in Proceedings of the American Control Conference, pp. 1880–1885, May 2002. View at Publisher · View at Google Scholar · View at Scopus
  30. W. Xiang and J. Xiao, “Discussion on stability, l2-gain and asynchronous H control of discrete-time switched systems with average dwell time,” IEEE Transactions on Automatic Control, vol. 57, no. 12, pp. 3259–3261, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. C. Cai, “Dwell-time approach to input-output stability properties for a class of discrete-time dynamical systems,” Systems & Control Letters, vol. 60, no. 6, pp. 383–389, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. J. C. Geromel and P. Colaneri, “H and dwell time specifications of continuous-time switched linear systems,” IEEE Transactions on Automatic Control, vol. 55, no. 1, pp. 207–212, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. P. Colaneri, P. Bolzern, and J. C. Geromel, “Root mean square gain of discrete-time switched linear systems under dwell time constraints,” Automatica, vol. 47, no. 8, pp. 1677–1684, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. K. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-Delay Systems, Springer, Berlin , Germany, 2003. View at MathSciNet
  35. 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
  36. B. Lu and F. Wu, “Switching LPV control designs using multiple parameter-dependent Lyapunov functions,” Automatica, vol. 40, no. 11, pp. 1973–1980, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus