Abstract and Applied Analysis

Resilient Robust Finite-Time L 2 - L Controller Design for Uncertain Neutral System with Mixed Time-Varying Delays

Xia Chen and Shuping He

Full-text: Open access

Abstract

The delay-dependent resilient robust finite-time L 2 - L control problem of uncertain neutral time-delayed system is studied. The disturbance input is assumed to be energy bounded and the time delays are time-varying. Based on the Lyapunov function approach and linear matrix inequalities (LMIs) techniques, a state feedback controller is designed to guarantee that the resulted closed-loop system is finite-time bounded for all uncertainties and to satisfy a given L 2 - L constraint condition. Simulation results illustrate the validity of the proposed approach.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 304824, 12 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412605742

Digital Object Identifier
doi:10.1155/2014/304824

Mathematical Reviews number (MathSciNet)
MR3212410

Citation

Chen, Xia; He, Shuping. Resilient Robust Finite-Time ${L}_{2}\text{-}{L}_{\infty }$ Controller Design for Uncertain Neutral System with Mixed Time-Varying Delays. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 304824, 12 pages. doi:10.1155/2014/304824. https://projecteuclid.org/euclid.aaa/1412605742


Export citation

References

  • S. He and F. Liu, “${L}_{2}\text{-}{L}_{\infty }$ fuzzy control for Markov jump systems with neutral time-delays,” Mathematics and Computers in Simulation, vol. 92, pp. 1–13, 2013.
  • J. Sun, G. P. Liu, J. Chen, and D. Rees, “Improved delay-range-dependent stability criteria for linear systems with time-varying delays,” Automatica, vol. 46, no. 2, pp. 466–470, 2010.
  • L. Vu and K. A. Morgansen, “Stability of time-delay feedback switched linear systems,” IEEE Transactions on Automatic Control, vol. 55, no. 10, pp. 2385–2390, 2010.
  • J. Hu, Z. Wang, H. Gao, and L. K. Stergioulas, “Robust ${H}_{\infty }$ sliding mode control for discrete time-delay systems with stochastic nonlinearities,” Journal of the Franklin Institute, vol. 349, no. 4, pp. 1459–1479, 2012.
  • 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.
  • D. Zhang and L. Yu, “${H}_{\infty }$ filtering for linear neutral systems with mixed time-varying delays and nonlinear perturbations,” Journal of the Franklin Institute, vol. 347, no. 7, pp. 1374–1390, 2010.
  • 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.
  • X.-G. Liu, M. Wu, R. Martin, and M.-L. Tang, “Delay-dependent stability analysis for uncertain neutral systems with time-varying delays,” Mathematics and Computers in Simulation, vol. 75, no. 1-2, pp. 15–27, 2007.
  • R. Rakkiyappan, P. Balasubramaniam, and R. Krishnasamy, “Delay dependent stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2147–2156, 2011.
  • P. Balasubramaniam, R. Krishnasamy, and R. Rakkiyappan, “Delay-dependent stability of neutral systems with time-varying delays using delay-decomposition approach,” Applied Mathematical Modelling, vol. 36, no. 5, pp. 2253–2261, 2012.
  • P. Dorato, “Short-time stability in linear time-varying systems,” in Proceedings of the IRE International Convention, pp. 83–87, 1961.
  • F. Amato, M. Ariola, and P. Dorato, “Finite-time control of linear systems subject to parametric uncertainties and disturbances,” Automatica, vol. 37, no. 9, pp. 1459–1463, 2001.
  • F. Amato, M. Ariola, and C. Cosentino, “Finite-time stabilization via dynamic output feedback,” Automatica, vol. 42, no. 2, pp. 337–342, 2006.
  • S. He and F. Liu, “Finite-time ${H}_{\infty }$ fuzzy control of nonlinear jump systems with time delays via dynamic observer-based state feedback,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 4, pp. 605–614, 2012.
  • J. Song and S. He, “Nonfragile robust finite-time ${L}_{2}\text{-}{L}_{\infty }$ controller design for a class of uncertain Lipschitz nonlinear systems with time-delays,” Abstract and Applied Analysis, vol. 2013, Article ID 265473, 9 pages, 2013.
  • D. A. Wilson, “Convolution and Hankel operator norms for linear systems,” in Proceedings of the 27th IEEE Conference on Decision and Control, pp. 1373–1374, IEEE, December 1988.
  • L. Xie, “Output feedback ${H}_{\infty }$ control of systems with parameter uncertainty,” International Journal of Control, vol. 63, no. 4, pp. 741–750, 1996. \endinput