Table of Contents Author Guidelines Submit a Manuscript
International Journal of Differential Equations
Volume 2014, Article ID 102653, 13 pages
http://dx.doi.org/10.1155/2014/102653
Research Article

Further Stability Analysis on Neutral Systems with Actuator Saturation and Time-Delays

Department of Automation, School of Information Science and Technology, University of Science and Technology of China, Anhui 230027, China

Received 13 January 2014; Revised 3 April 2014; Accepted 7 April 2014; Published 4 May 2014

Academic Editor: Kartik Ariyur

Copyright © 2014 Xinghua Liu. 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. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, Calif, USA, 1993. View at MathSciNet
  2. V. B. Kolmanovskii and A. Myshkis, Applied Theory of Functional Differential Equations, Kluwer Academic, Dordrecht, The Netherlands, 1999.
  3. S.-I. Niculescu, Delay Effects on Stability: A Robust Control Approach, vol. 269 of Lecture Notes in Control and Information Sciences, Springer, London, UK, 2001. View at Zentralblatt MATH · View at MathSciNet
  4. C.-H. Lien, “New stability criterion for a class of uncertain nonlinear neutral time-delay systems,” International Journal of Systems Science, vol. 32, no. 2, pp. 215–219, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. C.-H. Lien, K.-W. Yu, and J.-G. Hsieh, “Stability conditions for a class of neutral systems with multiple time delays,” Journal of Mathematical Analysis and Applications, vol. 245, no. 1, pp. 20–27, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. D. Ivănescu, S.-I. Niculescu, L. Dugard, J.-M. Dion, and E. I. Verriest, “On delay-dependent stability for linear neutral systems,” Automatica, vol. 39, no. 2, pp. 255–261, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. E. Fridman, “New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems,” Systems & Control Letters, vol. 43, no. 4, pp. 309–319, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. D. Chen, C.-H. Lien, K. K. Fan, and J. H. Chou, “Criteria for asymptotic stability of a class of neutral systems via a LMI approach,” IEE Proceedings: Control Theory and Applications, vol. 148, no. 6, pp. 442–447, 2001. View at Publisher · View at Google Scholar · View at Scopus
  9. J.-H. Park, “A new delay-dependent criterion for neutral systems with multiple delays,” Journal of Computational and Applied Mathematics, vol. 136, no. 1-2, pp. 177–184, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J.-H. Park, “Stability criterion for neutral differential systems with mixed multiple time-varying delay arguments,” Mathematics and Computers in Simulation, vol. 59, no. 5, pp. 401–412, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J.-H. Park, “Convex optimization approach to dynamic output feedback control for delay differential systems of neutral type,” Journal of Optimization Theory and Applications, vol. 127, no. 2, pp. 411–423, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J.-H. Park and S. Won, “Asymptotic stability of neutral systems with multiple delays,” Journal of Optimization Theory and Applications, vol. 103, no. 1, pp. 183–200, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J.-H. Park and S. Won, “A note on stability of neutral delay-differential systems,” Journal of the Franklin Institute, vol. 336, no. 3, pp. 543–548, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. O. M. Kwon, M. J. Park, J. H. Park, S. M. Lee, and E. J. Cha, “New delay-partitioning approaches to stability criteria for uncertain neutral systems with time-varying delays,” Journal of the Franklin Institute, vol. 349, no. 9, pp. 2799–2823, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. Q.-L. Han, “On delay-dependent stability for neutral delay-differential systems,” International Journal of Applied Mathematics and Computer Science, vol. 11, no. 4, pp. 965–976, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. Q.-L. Han, “Robust stability of uncertain delay-differential systems of neutral type,” Automatica, vol. 38, no. 4, pp. 719–723, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. S.-I. Niculescu, “On delay-dependent stability under model transformations of some neutral linear systems,” International Journal of Control, vol. 74, no. 6, pp. 609–617, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. A. Haurani, H. H. Michalska, and B. Boulet, “Delay-dependent robust stabilization of uncertain neutral systems with saturating actuators,” in Proceedings of the American Control Conference, pp. 509–514, Denver, Colo, USA, June 2003. View at Scopus
  19. A. H. Glattfelder and W. Schaufelberger, “Stability analysis of single loop control systems with saturation and antireset-windup circuits,” IEEE Transactions on Automatic Control, vol. 28, no. 12, pp. 1074–1081, 2003. View at Google Scholar · View at Scopus
  20. J.-J. Yan, J.-S. Lin, and T.-L. Liao, “Robust dynamic compensator for a class of time delay systems containing saturating control input,” Chaos, Solitons & Fractals, vol. 31, no. 5, pp. 1223–1231, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. J. M. G. da Silva Jr., A. Seuret, E. Fridman, and J. P. Richard, “Stabilisation of neutral systems with saturating control inputs,” International Journal of Systems Science, vol. 42, no. 7, pp. 1093–1103, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. P.-L. Liu, “Stabilization criteria for neutral time delay systems with saturating actuators,” Journal of the Franklin Institute, vol. 347, no. 8, pp. 1577–1588, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. P.-L. Liu and H.-L. Hung, “Stability of bilinear time-delay systems with saturating actuators,” in Proceedings of the IEEE International Symposium on Industrial Electronics (ISIE '99), pp. 1082–1086, Bled, Slovenia, July 1999. View at Scopus
  24. J. K. Hale and S. M. V. Lunel, Introduction to Functional-Differential Equations, vol. 99 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1993. View at MathSciNet
  25. S. A. Rodrìguez, J.-M. Dion, and L. Dugard, “Stability of neutral time delay systems: a survey of some results,” in Advances in Automatic Control, vol. 754, pp. 315–335, Kluwer Academic, Boston, Mass, USA, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. V. B. Kolmanovskii and J.-P. Richard, “Stability of some linear systems with delays,” IEEE Transactions on Automatic Control, vol. 44, no. 5, pp. 984–989, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. V. L. Kharitonov, “Robust stability analysis of time-delay systems: a survey,” in Proceedings of the IFAC Conference on System Structure and Control, pp. 1–12, Nantes, France, 1998.
  28. D. Yue, S. Won, and O. Kwon, “Delay dependent stability of neutral systems with time delay: an LMI approach,” IEE Proceedings: Control Theory and Applications, vol. 150, no. 1, pp. 23–27, 2003. View at Publisher · View at Google Scholar · View at Scopus
  29. H. B. Ji, Algebra Foundation of Control Theory, University of Science and Technology of China Press, Hefei, China, 2008.
  30. S. Tarbouriech, J. M. G. da Silva Jr., and G. Garcia, “Delay-dependent anti-windup strategy for linear systems with saturating inputs and delayed outputs,” International Journal of Robust and Nonlinear Control, vol. 14, no. 7, pp. 665–682, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. B. Yang, J. C. Wang, X. J. Pan, and C. Q. Zhong, “Delay-dependent criteria for robust stability of linear neutral systems with time-varying delay and nonlinear perturbations,” International Journal of Systems Science, vol. 38, no. 6, pp. 511–518, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. Y.-Y. Cao and J. Lam, “Computation of robust stability bounds for time-delay systems with nonlinear time-varying perturbations,” International Journal of Systems Science, vol. 31, no. 3, pp. 359–365, 2000. View at Publisher · View at Google Scholar · View at Scopus
  33. S.-I. Niculescu, J.-M. Dion, and L. Dugard, “Robust stabilization for uncertain time-delay systems containing saturating actuators,” IEEE Transactions on Automatic Control, vol. 41, no. 5, pp. 742–747, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet