Abstract and Applied Analysis

Absolute Stability of a Class of Nonlinear Singular Systems with Time Delay

Hong-Bing Zeng, Gang Chen, and Shen-Ping Xiao

Full-text: Open access

Abstract

This paper deals with the absolute stability for a class of nonlinear singular systems with time delay. By employing a new Lyapunov-Krasovskii functional with the idea of partitioning delay length, improved delay-dependent stability criteria are established. The resulting condition is formulated in terms of linear matrix inequalities (LMIs), which is easy to be verified by exiting LMI optimization algorithms. A numerical example is given to show the effectiveness of the proposed technique and its improvements over the existing results.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 927024, 6 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412605760

Digital Object Identifier
doi:10.1155/2014/927024

Mathematical Reviews number (MathSciNet)
MR3193559

Citation

Zeng, Hong-Bing; Chen, Gang; Xiao, Shen-Ping. Absolute Stability of a Class of Nonlinear Singular Systems with Time Delay. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 927024, 6 pages. doi:10.1155/2014/927024. https://projecteuclid.org/euclid.aaa/1412605760


Export citation

References

  • A. I. Lur'e, Some Nonlinear Problems in the Theory of Automatic Control, H.M. Stationery Office, 1957.
  • H. Shen, S. Xu, X. Song, and J. Luo, “Delay-dependent robust stabilization for uncertain stochastic switching systems with distributed delays,” Asian Journal of Control, vol. 11, no. 5, pp. 527–535, 2009.
  • H. Shen, S. Xu, J. Zhou, and J. Lu, “Fuzzy ${H}_{\infty }$ filtering for nonlinear Markovian jump neutral systems,” International Journal of Systems Science, vol. 42, no. 5, pp. 767–780, 2011.
  • H.-B. Zeng, Y. He, M. Wu, and S.-P. Xiao, “Absolute stability and stabilization for Lurie networked control systems,” International Journal of Robust and Nonlinear Control, vol. 21, no. 14, pp. 1667–1676, 2011.
  • M. Wu, Z. Y. Feng, and Y. He, “Improved delay-dependent absolute stability of Lur'e systems with time-delay,” International Journal of Control, Automation, and Systems, vol. 7, no. 6, pp. 1009–1014, 2009.
  • A. Kazemy and M. Farrokhi, “Robust absolute stability analysis of multiple time-delay Lur'e systems with parametric uncertainties,” Asian Journal of Control, vol. 15, no. 1, pp. 203–213, 2013.
  • Q.-L. Han, “Absolute stability of time-delay systems with sector-bounded nonlinearity,” Automatica, vol. 41, no. 12, pp. 2171–2176, 2005.
  • Y. He, M. Wu, J.-H. She, and G.-P. Liu, “Robust stability for delay Lur'e control systems with multiple nonlinearities,” Journal of Computational and Applied Mathematics, vol. 176, no. 2, pp. 371–380, 2005.
  • Q.-L. Han and D. Yue, “Absolute stability of Lur'e systems with time-varying delay,” IET Control Theory & Applications, vol. 1, no. 3, pp. 854–859, 2007.
  • 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.
  • Q.-L. Han, “A new delay-dependent absolute stability criterion for a class of nonlinear neutral systems,” Automatica, vol. 44, no. 1, pp. 272–277, 2008.
  • L. Dai, Singular Control Systems, Springer, Berlin, Germany, 1989.
  • C. Yang, Q. Zhang, and L. Zhou, “Generalised absolute stability analysis and synthesis for Lur'e-type descriptor systems,” IET Control Theory & Applications, vol. 1, no. 3, pp. 617–623, 2007.
  • S. Xu, P. van Dooren, R. Ştefan, and J. Lam, “Robust stability and stabilization for singular systems with state delay and parameter uncertainty,” IEEE Transactions on Automatic Control, vol. 47, no. 7, pp. 1122–1128, 2002.
  • Z.-G. Wu and W.-N. Zhou, “Delay-dependent robust stabilization for uncertain singular systems with state delay,” Acta Automatica Sinica, vol. 33, no. 7, pp. 714–718, 2007.
  • H. Wang, A. Xue, and R. Lu, “Absolute stability criteria for a class of nonlinear singular systems with time delay,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 2, pp. 621–630, 2009.
  • F. Gouaisbaut and D. Peaucelle, “Delay-dependent stability analysis of linear time delay systems,” in Proceedings of the 6th IFAC Workshop on Time-Delay Systems, 2006.
  • M. Krstić and H. Deng, Stabilization of Nonlinear Uncertain Systems, Springer, London, UK, 1998.
  • Z. Wu, H. Su, and J. Chu, “${H}_{\infty }$ filtering for singular Markovian jump systems with time delay,” International Journal of Robust and Nonlinear Control, vol. 20, no. 8, pp. 939–957, 2010.
  • I. R. Petersen and C. V. Hollot, “A Riccati equation approach to the stabilization of uncertain linear systems,” Automatica, vol. 22, no. 4, pp. 397–411, 1986.
  • H. K. Khalil, Nonlinear Systems, Prentice Hall, Englewood Cliffs, NJ, USA, 1996.
  • S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, Pa, USA, 1994. \endinput