Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays

Regular Papers Control Theory

Abstract

This paper considers the design problems of a delay-dependent robust and non-fragile guaranteed cost controller for singular systems with parameter uncertainties and time-varying delays in state and control input. The designed controller, under the possibility of feedback gain variations, can guarantee that a closed-loop system is regular, impulse-free, stable, an upper bound of guaranteed cost function, and non-fragility in spite of parameter uncertainties, time-varying delays, and controller fragility. The existence condition of the controller, the controller’s design method, the upper bound of guaranteed cost function, and the measure of non-fragility in the controller are proposed using the linear matrix inequality (LMI) technique. Finally, numerical examples are given to illustrate the effectiveness and less conservatism of the proposed design method.

Keywords

Delay-dependent stability guaranteed cost control non-fragile control singular systems 

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References

  1. [1]
    M. S. Mahmoud and N. F. Al-Muthairi, “Quadratic stabilization of continuous time systems with state delay and norm-bounded time-varying uncertainties,” IEEE Trans. on Automatic Control, vol. 39, no. 10, pp. 2135–2139, 1994.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    H. H. Choi and M. J. Chung, “Memoryless H controller design for linear systems with delayed state and control,” Automatica, vol. 31, pp. 917–919, 1995.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Y. Y. Cao, Y. X. Sun, and C. Cheng, “Delay-dependent robust stabilization of uncertain systems with multiple state delays,” IEEE Trans. on Automatic Control, vol. 43, pp. 1608–1621, 1998.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    J. Gao and B. Huang, “Delay-dependent robust guaranteed cost control of an uncertain system with state and input delay,” International Journal of Systems Science, vol. 36, pp. 19–26, 2005.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    E. Fridman and U. Shaked, “An improvement stabilization method for linear time-delay systems,” IEEE Trans. on Automatic Control, vol. 47, pp. 1931–1937, 2002.CrossRefMathSciNetGoogle Scholar
  6. [6]
    H. J. Gao and C. H. Wang, “Comments and further results on a descriptor system approach to H control of linear time-delay systems,” IEEE Trans. on Automatic Control, vol. 48, pp. 520–525, 2003.CrossRefMathSciNetGoogle Scholar
  7. [7]
    X. M. Zhang, M. Wu, J. H. She, and Y. He, “Delay-dependent stabilization of linear systems with time-varying state and input delays,” Automatica, vol. 41, pp. 1405–1412, 2005.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    S. S. L. Chang and T. K. C. Peng, “Adaptive guaranteed cost control of systems with uncertain parameters,” IEEE Trans. on Automatic Control, vol. 17, pp. 474–483, 1972.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Y. S. Lee, O. K. Kwon, and W. H. Kwon, “Delay-dependent guaranteed cost control for uncertain state delayed systems,” Int. Journal of Control, Automation, and Systems, vol. 3, pp. 524–532, 2005.Google Scholar
  10. [10]
    P. L. D. Peres, J. C. Geromel, and S. R. Souza, “H guaranteed cost control for uncertain continuous-time linear systems,” Systems and Control Lett., vol. 20, pp. 413–418, 1993.MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    L. Yu and J. Chu, “An LMI approach to guaranteed cost control of linear uncertain time delay system,” Automatica, vol. 35, pp. 1155–1159, 1999.MATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    I. Masubuchi, Y. Kamitane, A. Ohara, and N. Suda, “H control for descriptor systems: a matrix inequalities approach,” Automatica, vol. 33, pp. 669–673, 1997.MATHCrossRefMathSciNetGoogle Scholar
  13. [13]
    K. Takaba, N. Morihara, and T. Katayama, “A generalized Lyapunov theorem for descriptor system,” System and Control Lett., vol. 24, pp. 49–51, 1995.MATHCrossRefGoogle Scholar
  14. [14]
    D. Yue and J. Lam, “Non-fragile guaranteed cost control for uncertain descriptor systems with time-varying state and input delays,” Optimal Control Appl. Methods, vol. 26, pp. 85–105, 2005.CrossRefMathSciNetGoogle Scholar
  15. [15]
    R. X. Zhong and Z. Yang, “Delay-dependent robust control of descriptor systems with time delay,” Asian Journal of Control, vol. 8, pp. 36–44, 2006.MathSciNetGoogle Scholar
  16. [16]
    H. L. Gao, Z. S. Q, Z. L. Cheng, and B. G. Xu, “Delay-dependent state feedback guaranteed cost control uncertain singular time delay systems,” Proc. of IEEE Conf. on Decision and Control, and European Control Conf., pp. 4354–4359, 2005.Google Scholar
  17. [17]
    Z. G. Wu and W. N. Zhou, “Delay-dependent robust stabilization for uncertain singular systems with state delay,” Acta Automatica Sinica, vol. 33, pp. 714–718, 2007.MATHMathSciNetGoogle Scholar
  18. [18]
    P. Dorato, C. T. Abdallah, and D. Famularo, “On the design of non-fragile compensators via symbolic quantifier elimination,” World Automation Congress, pp. 9–14, 1998.Google Scholar
  19. [19]
    L. H. Keel and S. P. Bhattacharyya, “Robust, fragile, or optimal,” IEEE Trans. Automat. Contr., vol. 42, pp. 1098–1105, 1997.MATHCrossRefMathSciNetGoogle Scholar
  20. [20]
    W. M. Haddad and J. Corrado, “Non-fragile controller design via quadratic Lyapunov bounds,” Proc. IEEE Control Decision on Conference, 1997.Google Scholar
  21. [21]
    G. H. Yang and J. L. Wang, “Non-fragile H control for linear systems with multiplicative controller gain variations,” Automatica, vol. 37, pp. 727–737, 2001.MATHGoogle Scholar
  22. [22]
    I. R. Petersen, “A stabilization algorithm for a class of uncertain linear systems,” Systems and Control Lett., vol. 8, pp. 351–357, 1987.MATHCrossRefMathSciNetGoogle Scholar
  23. [23]
    X. L. Zhu and G. H. Yang, “Delay-dependent stability criteria for systems with differentiable time delays,” Acta Automatica Sinica, vol. 34, pp. 765–771, 2008.MATHCrossRefMathSciNetGoogle Scholar
  24. [24]
    X. L. Zhu and G. H. Yang, “Jensen integral inequality approach to stability analysis of continuous-time systems with time-varying delay,” IET Control Theory Appl., vol. 2, no. 6, pp. 524–534, 2008.CrossRefMathSciNetGoogle Scholar

Copyright information

© The Institute of Control, Robotics and Systems Engineers and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg GmbH 2009

Authors and Affiliations

  1. 1.Division of Electronic EngineeringSun Moon UniversityChungnamKorea

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