Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 238487, 8 pages
http://dx.doi.org/10.1155/2014/238487
Research Article

Simplified Stability Criteria for Delayed Neutral Systems

1School of Mathematical Science, Heilongjiang University, Harbin 150080, China
2College of Computer and Information Engineering, Heilongjiang University of Science and Technology, Harbin 150022, China

Received 4 March 2014; Accepted 1 April 2014; Published 13 May 2014

Academic Editor: Yuxin Zhao

Copyright © 2014 Xinghua Zhang 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. V. B. Kolmanovskii and A. Myshkis, Applied Theory of Functional Differential Equations, Kluwer Academic Publishers, Boston, Mass, USA, 1992. View at Publisher · View at Google Scholar
  2. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, vol. 191 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1993. View at MathSciNet
  3. S.-I. Niculescu, Delay Effects on Stability, vol. 269 of Lecture Notes in Control and Information Sciences, Springer, Berlin, Germany, 2001. View at MathSciNet
  4. X. Lin, X. Zhang, and Y. Wang, “Robust passive filtering for neutral-type neural networks with time-varying discrete and unbounded distributed delays,” Journal of the Franklin Institute, vol. 350, no. 5, pp. 966–989, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  5. X. Zhang, X. Lin, and Y. Wang, “Robust fault detection filter design for a class of neutral-type neural networks with time-varying discrete and unbounded distributed delays,” Optimal Control Applications & Methods, vol. 34, no. 5, pp. 590–607, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  6. Y. Wang, X. Zhang, and Y. Hu, “Robust H control for a class of uncertain neutral stochastic systems with mixed delays: A CCL approach,” Circuits, Systems, and Signal Processing, vol. 32, no. 2, pp. 631–646, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  7. Y. Wang, X. Zhang, and Y. He, “Improved delay-dependent robust stability criteria for a class of uncertain mixed neutral and Lur'e dynamical systems with interval time-varying delays and sector-bounded nonlinearity,” Nonlinear Analysis: Real World Applications, vol. 13, no. 5, pp. 2188–2194, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. G. D. Zhang, X. Lin, and X. Zhang, “Exponential stabilization of neutral-type neural networks with mixed interval time-varying delays by intermittent control: a CCL approach,” Circuits, Systems and Signal Processing, vol. 33, pp. 371–391, 2014. View at Publisher · View at Google Scholar
  9. 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
  10. 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
  11. Y. He, Q.-G. Wang, C. Lin, and M. Wu, “Augmented Lyapunov functional and delay-dependent stability criteria for neutral systems,” International Journal of Robust and Nonlinear Control, vol. 15, no. 18, pp. 923–933, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. M. Wu, Y. He, and J.-H. She, “New delay-dependent stability criteria and stabilizing method for neutral systems,” IEEE Transactions on Automatic Control, vol. 49, no. 12, pp. 2266–2271, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  13. J. Sun, G. P. Liu, and J. Chen, “Delay-dependent stability and stabilization of neutral time-delay systems,” International Journal of Robust and Nonlinear Control, vol. 19, no. 12, pp. 1364–1375, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. W. Qian, J. Liu, and S. Fei, “Augmented Lyapunov functional approach for stability of neutral systems with mixed delays,” Asian Journal of Control, vol. 14, no. 2, pp. 572–579, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  15. 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
  16. C.-H. Lien and J.-D. Chen, “Discrete-delay-independent and discrete-delay-dependent criteria for a class of neutral systems,” Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, vol. 125, no. 1, pp. 33–41, 2003. View at Publisher · View at Google Scholar · View at Scopus
  17. H. Chen, Y. Zhang, and Y. Zhao, “Stability analysis for uncertain neutral systems with discrete and distributed delays,” Applied Mathematics and Computation, vol. 218, no. 23, pp. 11351–11361, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. J. H. Park and O. Kwon, “On new stability criterion for delay-differential systems of neutral type,” Applied Mathematics and Computation, vol. 162, no. 2, pp. 627–637, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. Q.-L. Han, “On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty,” Automatica, vol. 40, no. 6, pp. 1087–1092, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  20. Q.-L. Han, “A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays,” Automatica, vol. 40, no. 10, pp. 1791–1796, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  21. Y. He, M. Wu, J.-H. She, and G.-P. Liu, “Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays,” Systems & Control Letters, vol. 51, no. 1, pp. 57–65, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. O. M. Kwon, J. H. Park, and S. M. Lee, “On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays,” Applied Mathematics and Computation, vol. 197, no. 2, pp. 864–873, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. S. Xu, J. Lam, and Y. Zou, “Further results on delay-dependent robust stability conditions of uncertain neutral systems,” International Journal of Robust and Nonlinear Control, vol. 15, no. 5, pp. 233–246, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. E. Fridman and U. Shaked, “A descriptor system approach to H control of linear time-delay systems,” IEEE Transactions on Automatic Control, vol. 47, no. 2, pp. 253–270, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  25. X.-G. Liu, M. Wu, R. Martin, and M.-L. Tang, “Stability analysis for neutral systems with mixed delays,” Journal of Computational and Applied Mathematics, vol. 202, no. 2, pp. 478–497, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. Z. Zhao, W. Wang, and B. Yang, “Delay and its time-derivative dependent robust stability of neutral control system,” Applied Mathematics and Computation, vol. 187, no. 2, pp. 1326–1332, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. W. Qian, J. Liu, Y. Sun, and S. Fei, “A less conservative robust stability criteria for uncertain neutral systems with mixed delays,” Mathematics and Computers in Simulation, vol. 80, no. 5, pp. 1007–1017, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. K. Gu and S.-I. Niculescu, “Further remarks on additional dynamics in various model transformations of linear delay systems,” IEEE Transactions on Automatic Control, vol. 46, no. 3, pp. 497–500, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional-Differential Equations, vol. 99 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1993. View at MathSciNet
  30. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15 of SIAM Studies in Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  31. P. Gahinet and P. Apkarian, “A linear matrix inequality approach to H control,” International Journal of Robust and Nonlinear Control, vol. 4, no. 4, pp. 421–448, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. H. Zhu, X. Zhang, and S. Cui, “Further results on H control for discrete-time uncertain singular systems with interval time-varying delays in state and input,” Optimal Control Applications & Methods, vol. 34, no. 3, pp. 328–347, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. F. Li and X. Zhang, “A delay-dependent bounded real lemma for singular LPV systems with time-variant delay,” International Journal of Robust and Nonlinear Control, vol. 22, no. 5, pp. 559–574, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. F. B. Li, P. Shi, L. G. Wu, and X. Zhang, “Fuzzy-model-based D-stability and non-fragile control for discrete-time descriptor systems with multiple delays,” IEEE Transactions on Fuzzy Systems, 2013. View at Publisher · View at Google Scholar
  35. X. Zhang and H. Zhu, “Robust stability and stabilization criteria for discrete singular time-delay LPV systems,” Asian Journal of Control, vol. 14, no. 4, pp. 1084–1094, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  36. L. G. Wu, W. X. Zheng, and H. J. Gao, “Dissipativity-based sliding mode control of switched stochastic systems,” IEEE Transactions on Automatic Control, vol. 58, no. 3, pp. 785–791, 2013. View at Publisher · View at Google Scholar
  37. L. Wu, X. Su, and P. Shi, “Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems,” Automatica, vol. 48, no. 8, pp. 1929–1933, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  38. F. B. Li, L. G. Wu, and P. Shi, “Stochastic stability of semi-Markovian jump systems with mode-dependent delays,” International Journal of Robust and Nonlinear Control, 2013. View at Publisher · View at Google Scholar
  39. Y. T. Wang, A. H. Yu, and X. Zhang, “Robust stability of stochastic genetic regulatory networks with time-varying delays: a delay fractioning approach,” Neural Computing and Applications, vol. 23, no. 5, pp. 1217–1227, 2013. View at Publisher · View at Google Scholar
  40. L. L. Chen, Y. Zhou, and X. Zhang, “Guaranteed cost control for uncertain genetic regulatory networks with interval time-varying delays,” Neurocomputing, vol. 131, pp. 105–112, 2014. View at Publisher · View at Google Scholar
  41. X. Zhang, A. H. Yu, and G. D. Zhang, “M-matrix-based delay-range-dependent global asymptotical stability criterion for genetic regulatory networks with time-varying delays,” Neurocomputing, vol. 113, pp. 8–15, 2013. View at Publisher · View at Google Scholar