Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 125343, 10 pages
http://dx.doi.org/10.1155/2015/125343
Research Article

Robust Stabilization and Disturbance Rejection of Positive Systems with Time-Varying Delays and Actuator Saturation

1School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
2School of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, China

Received 11 June 2014; Accepted 17 August 2014

Academic Editor: Mohammed Chadli

Copyright © 2015 Xi Ding 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. 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
  2. R. Shorten, D. Leith, J. Foy, and R. Kilduff, “Towards an analysis and design framework for congestion control in communication networks,” in Proceeding of the 12th Yale Workshop on Adaptive and Learning Systems, 2003.
  3. 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
  4. 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
  5. M. Bolajraf, F. Tadeo, T. Alvarez, and M. A. Rami, “State-feedback with memory for controlled positivity with application to congestion control,” IET Control Theory & Applications, vol. 4, no. 10, pp. 2041–2048, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. 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
  7. T. Kaczorek, “The choice of the forms of Lyapunov functions for a positive 2D Roesser model,” International Journal of Applied Mathematics and Computer Science, vol. 17, no. 4, pp. 471–475, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. T. Kaczorek, “A realization problem for positive continuous-time systems with reduced numbers of delays,” International Journal of Applied Mathematics and Computer Science, vol. 16, no. 3, pp. 325–331, 2006. View at Google Scholar · View at MathSciNet · View at Scopus
  9. L. Benvenuti, A. D. Santis, and L. Farina, Positive Systems: Theory and Applications, Springer, New York, NY, USA, 2003.
  10. M. A. Rami, F. Tadeo, and A. Benzaouia, “Control of constrained positive discrete systems,” in Proceedings of the American Control Conference (ACC '07), pp. 5851–5856, New York, NY, USA, July 2007. View at Publisher · View at Google Scholar · View at Scopus
  11. F. Knorn, O. Mason, and R. Shorten, “On linear co-positive Lyapunov functions for sets of linear positive systems,” Automatica, vol. 45, no. 8, pp. 1943–1947, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. S. Li, Z. Xiang, and H. R. Karimi, “Stability and L1-gain controller design for positive switched systems with mixed time-varying delays,” Applied Mathematics and Computation, vol. 222, pp. 507–518, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. H. Liu, P. Shi, H. R. Karimi, and M. Chadli, “Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay,” International Journal of Systems Science, 2014. View at Publisher · View at Google Scholar
  14. H. R. Karimi and H. Gao, “New delay-dependent exponential H synchronization for uncertain neural networks with mixed time delays,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 40, no. 1, pp. 173–185, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. F. Zhang and Y. Zhang, “State estimation of neural networks with both time-varying delays and norm-bounded parameter uncertainties via a delay decomposition approach,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 12, pp. 3517–3529, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. Z. C. Qin, S. Zhong, and J. Q. Sun, “Sliding mode control experiments of uncertain dynamical systems with time delay,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 12, pp. 3558–3566, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. M. S. Mahmoud and P. Shi, “Robust stability, stabilization and H control of time-delay systems with Markovian jump parameters,” International Journal of Robust and Nonlinear Control, vol. 13, no. 8, pp. 755–784, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. Y. Sun, “Delay-independent stability of switched linear systems with unbounded time-varying delays,” Abstract and Applied Analysis, vol. 2012, Article ID 560897, 11 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  19. M. Xiang and Z. Xiang, “Stability, L1-gain and control synthesis for positive switched systems with time-varying delay,” Nonlinear Analysis: Hybrid Systems, vol. 9, no. 1, pp. 9–17, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. X. Liu and C. Dang, “Stability analysis of positive switched linear systems with delays,” IEEE Transactions on Automatic Control, vol. 56, no. 7, pp. 1684–1690, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. X. Zhao, L. Zhang, and P. Shi, “Stability of a class of switched positive linear time-delay systems,” International Journal of Robust and Nonlinear Control, vol. 23, no. 5, pp. 578–589, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. C. Briat, “Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L1-gain and L-gain characterization,” International Journal of Robust and Nonlinear Control, vol. 23, no. 17, pp. 1932–1954, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. M. Xiang and Z. Xiang, “Observer design of switched positive systems with time-varying delays,” Circuits, Systems, and Signal Processing, vol. 32, no. 5, pp. 2171–2184, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. 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
  25. Z. Duan, H. R. Karimi, and Z. Xiang, “Stability and l1-gain analysis for positive 2D systems with state delays in the Roesser model,” Mathematical Problems in Engineering, vol. 2013, Article ID 169713, 10 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  26. S. Li, Z. Xiang, and H. R. Karimi, “Finite-time L1-gain control for positive switched systems with time-varying delay via delta operator approach,” Abstract and Applied Analysis, vol. 2014, Article ID 872158, 11 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. S. Li, Z. Xiang, and H. R. Karimi, “Positive L1 observer design for positive switched systems,” Circuits, Systems, and Signal Processing, vol. 33, no. 7, pp. 2085–2106, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  28. Z. Duan, Z. Xiang, and H. R. Karimi, “Delay-dependent exponential stabilization of positive 2D switched state-delayed systems in the Roesser model,” Information Sciences, vol. 272, pp. 173–184, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. X. Zhang, M. Wang, and J. Zhao, “Stability analysis and anti-windup design of uncertain discrete-time switched linear systems subject to actuator saturation,” Journal of Control Theory and Applications, vol. 10, no. 3, pp. 325–331, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. D. Saifia, M. Chadli, H. R. Karimi, and S. Labiod, “Fuzzy control for Electric Power Steering SYStem with assist motor current input constraints,” Journal of the Franklin Institute: Engineering and Applied Mathematics, vol. 352, no. 2, pp. 562–576, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  31. S. Oucheriah, “Global stabilization of a class of linear continuous time-delay systems with saturating controls,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 43, no. 12, pp. 1012–1015, 1996. View at Publisher · View at Google Scholar · View at Scopus
  32. S. Tarbouriech and J. M. G. da Silva Jr., “Synthesis of controllers for continuous-time delay systems with saturating controls via LMI's,” IEEE Transactions on Automatic Control, vol. 45, no. 1, pp. 105–111, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. Y.-Y. Cao, Z. Lin, and T. Hu, “Stability analysis of linear time-delay systems subject to input saturation,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 49, no. 2, pp. 233–240, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. S. Oucheriah, “Synthesis of controllers for time-delay systems subject to actuator saturation and disturbance,” Transactions of the ASME—Journal of Dynamic Systems, Measurement and Control, vol. 125, no. 2, pp. 244–249, 2003. View at Publisher · View at Google Scholar · View at Scopus
  35. E. Tissir and A. Hmamed, “Further results on the stabilization of time delay systems containing saturating actuators,” International Journal of Systems Science, vol. 23, no. 4, pp. 615–622, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  36. H. Fang, Z. Lin, and T. Hu, “Analysis of linear systems in the presence of actuator saturation and L2-disturbances,” Automatica, vol. 40, no. 7, pp. 1229–1238, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  37. Q. Zheng and F. Wu, “Output feedback control of saturated discrete-time linear systems using parameter-dependent Lyapunov functions,” Systems & Control Letters, vol. 57, no. 11, pp. 896–903, 2008. View at Publisher · View at Google Scholar · View at Scopus
  38. Y.-Y. Cao, Z. Lin, and D. G. Ward, “An antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation,” IEEE Transactions on Automatic Control, vol. 47, no. 1, pp. 140–145, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  39. T. Hu, Z. Lin, and B. M. Chen, “Analysis and design for discrete-time linear systems subject to actuator saturation,” Systems & Control Letters, vol. 45, no. 2, pp. 97–112, 2002. View at Publisher · View at Google Scholar · View at Scopus
  40. J. M. Gomes da Silva Jr. and S. Tarbouriech, “Anti-windup design with guaranteed regions of stability for discrete-time linear systems,” Systems & Control Letters, vol. 55, no. 3, pp. 184–192, 2006. View at Publisher · View at Google Scholar · View at Scopus
  41. D. Saifia, M. Chadli, S. Labiod, and T. M. Guerra, “Robust H static output feedback stabilization of T-S fuzzy systems subject to actuator saturation,” International Journal of Control, Automation and Systems, vol. 10, no. 3, pp. 613–622, 2012. View at Publisher · View at Google Scholar · View at Scopus
  42. J. Gomes da Silva and S. Tarbouriech, “Antiwindup design with guaranteed regions of stability: an LMI-based approach,” IEEE Transactions on Automatic Control, vol. 50, no. 1, pp. 106–111, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  43. J. Zhang, Y. Wu, Y. Wang, and Z. Gao, “Stability analysis and controller design of positive linear systems subject to actuator saturation,” in Proceedings of the 32nd Chinese Control Conference (CCC '13), pp. 33–38, Xi'an, China, July 2013.
  44. J.-S. Zhang, Z. Deng, and Y.-W. Wang, “Robust stability and stabilization of positive interval systems subject to actuator saturation,” Asian Journal of Control, vol. 16, no. 5, pp. 1553–1560, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  45. O. Mason and R. Shorten, “On linear copositive Lyapunov functions and the stability of switched positive linear systems,” IEEE Transactions on Automatic Control, vol. 52, no. 7, pp. 1346–1349, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  46. T. Hu, Z. Lin, and B. M. Chen, “An analysis and design method for linear systems subject to actuator saturation and disturbance,” Automatica, vol. 38, no. 2, pp. 351–359, 2002. View at Publisher · View at Google Scholar · View at Scopus