- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 793686, 9 pages
Wirtinger-Type Inequality and the Stability Analysis of Delayed Lur'e System
1College of Computer Science and Information, GuiZhou University, Guiyang, Guizhou 550025, China
2School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, Guizhou 550004, China
3College of Science, Guizhou University, Guiyang, Guizhou 550025, China
Received 11 May 2013; Revised 26 July 2013; Accepted 27 July 2013
Academic Editor: M. De la Sen
Copyright © 2013 Zixin Liu 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.
- A. I. Lur'e, Some Nonliear Problem in the Theory of Automatic Control, H.M. Stationary Office, London, UK, 1975.
- 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.
- S. Lun and Z. Tai, “Dissipativity for Lur'e distributed parameter control systems,” Applied Mathematics Letters, vol. 25, no. 4, pp. 682–686, 2012.
- Y. He and M. Wu, “Absolute stability for multiple delay general Lur'e control systems with multiple nonlinearities,” Journal of Computational and Applied Mathematics, vol. 159, no. 2, pp. 241–248, 2003.
- Q.-L. Han, “Absolute stability of time-delay systems with sector-bounded nonlinearity,” Automatica, vol. 41, no. 12, pp. 2171–2176, 2005.
- J. Cao and S. Zhong, “New delay-dependent condition for absolute stability of Lurie control systems with multiple time-delays and nonlinearities,” Applied Mathematics and Computation, vol. 194, no. 1, pp. 250–258, 2007.
- A. I. Zečević, E. Cheng, and D. D. Šiljak, “Control design for large-scale Lur'e systems with arbitrary information structure constraints,” Applied Mathematics and Computation, vol. 217, no. 3, pp. 1277–1286, 2010.
- V. A. Yakubovich, G. A. Leonov, and A. Kh. Gelig, Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities, vol. 14 of Series on Stability, Vibration and Control of Systems, World Scientific, River Edge, NJ, USA, 2004.
- F. Hao, “Absolute stability of uncertain discrete Lur'e systems and maximum admissible perturbed bounds,” Journal of the Franklin Institute, vol. 347, no. 8, pp. 1511–1525, 2010.
- Z. Tai and S. Lun, “Absolutely exponential stability of Lur'e distributed parameter control systems,” Applied Mathematics Letters, vol. 25, no. 3, pp. 232–236, 2012.
- J. Huang, Z. Han, X. Cai, and L. Liu, “Adaptive full-order and reduced-order observers for the Lur'e differential inclusion system,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 7, pp. 2869–2879, 2011.
- S. M. Lee and J. H. Park, “Delay-dependent criteria for absolute stability of uncertain time-delayed Lur'e dynamical systems,” Journal of the Franklin Institute, vol. 347, no. 1, pp. 146–153, 2010.
- J. G. Park, “A delay-dependent stability criterion for systems with un-certain linear state-delayed systems,” IEEE Transactions on Automatic Control, vol. 35, pp. 878–877, 1999.
- E. Fridman and U. Shaked, “-control of linear state-delay descriptor systems: an LMI approach,” Linear Algebra and its Applications, vol. 351-352, pp. 271–302, 2002.
- C. Yin, S.-m. Zhong, and W.-f. Chen, “On delay-dependent robust stability of a class of uncertain mixed neutral and Lur'e dynamical systems with interval time-varying delays,” Journal of the Franklin Institute, vol. 347, no. 9, pp. 1623–1642, 2010.
- 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.
- L. El Ghaoui and H. Lebret, “Robust solutions to least-squares problems with uncertain data,” SIAM Journal on Matrix Analysis and Applications, vol. 18, no. 4, pp. 1035–1064, 1997.
- K. Gu, “An integral inequality in the stability problem of time-delay systems,” in Proceedings of the 39th IEEE Confernce on Decision and Control (CDC '00), pp. 2805–2810, Sydney, Australia, December 2000.
- B. J. Xu and X. X. Liao, “Absolute stability criteria of delay-dependent for Lurie control systems,” Acta Automatica Sinica, vol. 28, no. 2, pp. 317–320, 2002.
- S. Zhou and J. Lam, “Robust stabilization of delayed singular systems with linear fractional parametric uncertainties,” Circuits, Systems, and Signal Processing, vol. 22, no. 6, pp. 579–588, 2003.
- J. Tian, S. Zhong, and L. Xiong, “Delay-dependent absolute stability of Lurie control systems with multiple time-delays,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 379–384, 2007.
- X. H. Nian, “Delay dependent conditions for absolute stability of Lur'e type control systems,” Acta Automatica Sinica, vol. 25, no. 4, pp. 556–564, 1999.
- D.-Y. Chen and W.-H. Liu, “Delay-dependent robust stability for Lurie control systems with multiple time-delays,” Control Theory and Applications, vol. 22, no. 3, pp. 499–502, 2005.
- B. Yang and M. Chen, “Delay-dependent criterion for absolute stability of Lurie type control systems with time delay,” Control Theory & Applications, vol. 18, no. 6, pp. 929–931, 2001.
- 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.
- S. Xu and G. Feng, “Improved robust absolute stability criteria for uncertain time-delay systems,” IET Control Theory and Applications, vol. 1, no. 6, pp. 1630–1637, 2007.
- S. J. Choi, S. M. Lee, S. C. Won, and J. H. Park, “Improved delay-dependent stability criteria for uncertain Lur'e systems with sector and slope restricted nonlinearities and time-varying delays,” Applied Mathematics and Computation, vol. 208, no. 2, pp. 520–530, 2009.