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access icon free Robust regional eigenvalue-clustering analysis for grey discrete-time systems with/without state delay

  • Author(s): Shinn-Horng Chen 1 ; Jyh-Horng Chou 1, 2, 3 ; Liang-An Zheng 1
    • View affiliations
    • Affiliations: 1: Department of Mechanical/Electrical Engineering, National Kaohsiung University of Applied Sciences, 415 Chien-Kung Road, Kaohsiung 807, Taiwan;
      2: Department of Mechanical and Automation Engineering, Institute of Electrical Engineering, National Kaohsiung First University of Science and Technology, 1 University Road, Yenchao, Kaohsiung 824, Taiwan;
      3: Department of Healthcare Administration and Medical Informatics, Kaohsiung Medical University, 100 Shi-Chuan 1st Road, Kaohsiung 807, Taiwan
  • Source: Volume 8, Issue 2, 16 January 2014, p. 94 – 103
    DOI:  10.1049/iet-cta.2013.0670 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 21/02/2013, Accepted 30/09/2013, Revised 10/09/2013, Published

The regional eigenvalue-clustering robustness problem of grey discrete-time systems with/without state delay is considered. Based on both spectral radius approach and matrix measure approach, three new sufficient conditions are proposed to preserve the regional eigenvalue-clustering property of grey discrete-time systems with/without state delay. If all eigenvalues are only required to be located within the unit circle, the proposed criteria become stability criteria. The proposed sufficient conditions are mathematically proven to be less conservative than those reported in the literature. Three examples are given to demonstrate that the proposed sufficient conditions are applicable and obtain less conservative results compared with those reported recently in the literature.

Inspec keywords: robust control; eigenvalues and eigenfunctions; delays; matrix algebra; discrete time systems; grey systems

Other keywords: matrix measure approach; regional eigenvalue-clustering robustness problem; sufficient conditions; unit circle; grey discrete-time systems; stability criteria; state delay; robust regional eigenvalue-clustering analysis; regional eigenvalue-clustering property; spectral radius approach

Subjects: Combinatorial mathematics; Algebra; Distributed parameter control systems; Stability in control theory; Discrete control systems

References

    1. 1)
      • 32. Chou, J.H., Chen, S.H., Fung, R.F.: ‘Sufficient conditions for the controllability of linear descriptor systems with both time-varying structured and unstructured parameter uncertainties’, IMA J. Math. Control Inf., 2001, 18, pp. 469–477 (doi: 10.1093/imamci/18.4.469).
    2. 2)
      • 6. Shyr, W.J., Hsu, C.H.: ‘Stability analysis of grey discrete time-delay systems: a sufficient condition’, in JordAin, M.A. (Ed.): ‘Discrete time systems’ (InTech Europe, Rijeka, Croatia, 2011), pp. 327–336.
    3. 3)
      • 3. Liu, S.F., Forrest, J., Yang, Y.J.: ‘A brief introduction to grey systems theory’. Proc. 2011 IEEE Int. Conf. Grey Systems and Intelligent Services, Naijing, China, 2011, pp. 1–9.
    4. 4)
      • 2. Liu, S.F., Forrest, J.: ‘Advances in grey systems theory and its applications’. Proc. 2007 IEEE Int. Conf. Grey Systems and Intelligent Services, Naijing, China, 2007, pp. 1–6.
    5. 5)
      • 24. He, S.A., Fong, I.K.: ‘Time-delay effects on controllability in LTI systems’. Proc. ICROS-SICE Int. Joint Conf., Fukuoka, Japan, 2009, pp. 327–332.
    6. 6)
      • 19. Chen, S.H., Chou, F.I., Chou, J.H.: ‘On robust controllability of linear systems with multiple delays in control’, IET Control Theory Appl., 2012, 6, pp. 1552–1556 (doi: 10.1049/iet-cta.2011.0486).
    7. 7)
      • 22. Ding, L., Yu, P., Liu, Z.W., Guan, Z.H.: ‘Consensus and performance optimisation of multi-agent systems with position-only information via impulsive control’, IET Control Theory Appl., 2013, 7, pp. 16–24 (doi: 10.1049/iet-cta.2012.0461).
    8. 8)
      • 12. Barmish, B.R.: ‘New tools for robustness of linear systems’ (Macmillan Publishing Company, 1994).
    9. 9)
      • 28. Juang, Y.T.: ‘Allowable perturbations for robust pole assignment of dynamic systems’. Proc. 26th IEEE Conf. Decision and Control, Los Angeles, USA, pp. 1319–1323.
    10. 10)
      • 11. Yedavalli, R.K.: ‘Robust root clustering for linear uncertain systems using generalized Lyapunov theory’, Automatica, 1993, 29, pp. 237–240 (doi: 10.1016/0005-1098(93)90188-Y).
    11. 11)
      • 29. Juang, Y.T., Kuo, T.S., Hsu, C.F.: ‘Stability robustness analysis of digital control systems in state-space models’, Int. J. Control, 1987, 46, pp. 1547–1556 (doi: 10.1080/00207178708933993).
    12. 12)
      • 23. Liu, P.L.: ‘Robustness of pole assignment in a specified circular region for discrete-time grey systems’, Int. J. Syst. Sci., 2001, 32, pp. 269–272 (doi: 10.1080/00207720120717).
    13. 13)
      • 20. Sipahi, R., Qiao, W.: ‘Responsible eigenvalue concept for the stability of a class of single-delay consensus dynamics with fixed topology’, IET Control Theory Appl., 2011, 5, pp. 622–629 (doi: 10.1049/iet-cta.2010.0202).
    14. 14)
      • 7. Gutman, S., Jury, E.I.: ‘A general theory for matrix root-clustering in subregions of the complex plane’, IEEE Trans. Autom. Control, 1981, 26, pp. 853–863 (doi: 10.1109/TAC.1981.1102764).
    15. 15)
      • 26. Kang, T.L., Shyr, W.J., Liu, P.L.: ‘D-pole placement robustness for perturbed grey discrete-time-delay systems’, Int. J. Syst. Sci., 2001, 32, pp. 639–642.
    16. 16)
      • 5. Liu, P.L., Shyr, W.J.: ‘Another sufficient condition for the stability of grey discrete-time systems’, J. Franklin Inst., 2005, 342, pp. 15–23 (doi: 10.1016/j.jfranklin.2004.07.008).
    17. 17)
      • 10. Horng, I.R., Horng, H.Y., Chou, J.H.: ‘Eigenvalue clustering in subregions of the complex plane for interval dynamic systems’, Int. J. Syst. Sci., 1993, 24, pp. 901–914 (doi: 10.1080/00207729308949532).
    18. 18)
      • 16. Chen, S.H., Chou, J.H., Zheng, L.A.: ‘Robust regional eigenvalue-clustering analysis for linear discrete singular time-delay systems with structured parameter uncertainties’, Trans. ASME, J. Dyn. Syst. Meas. Control, 2007, 129, pp. 83–90 (doi: 10.1115/1.2397156).
    19. 19)
      • 13. Wang, S.G., Shieh, L.S.: ‘A general theory for analysis and design of robust pole clustering in subregions of the complex plane’. Proc. 1994 Am. Control Conf., 1994, 1, pp. 627–636.
    20. 20)
      • 8. Monsour, M.: ‘Robust stability of interval matrices’. Proc. 28th IEEE Conf. Decision and Control, Florida, USA, 1989, pp. 46–51.
    21. 21)
      • 4. Zhou, C.S., Deng, J.L.: ‘Stability analysis of grey discrete-time systems’, IEEE Trans. Autom. Control, 1989, 34, pp. l73–175.
    22. 22)
      • 15. Wang, S.G., Lin, S., Shieh, L.: ‘Several simple sufficient conditions for Hurwitz and Schur stability of interval matrices’. Proc. IASTED Int. Conf. Control, Cancun, Mexico, 1997, pp. 31–34.
    23. 23)
      • 14. Bhattacharyya, S.P., Chapellat, H., Keel, L.H.: ‘Robust control: the parametric approach’ (Prentice-Hall, Upper Saddle River, NJ, 1995).
    24. 24)
      • 1. Deng, J.L.: ‘Control problems of grey systems’, Syst. Control Lett., 1982, 5, pp. 288–294.
    25. 25)
      • 21. Luo, J., Zou, X., Cao, C.: ‘Eigenvalue assignment for linear time-varying systems with disturbances’, IET Control Theory Appl., 2012, 6, pp. 365–374 (doi: 10.1049/iet-cta.2011.0039).
    26. 26)
      • 25. Liu, P.L.: ‘Stability of continuous and discrete time-delay grey systems’, Int. J. Syst. Sci., 2001, 32, pp. 947–952 (doi: 10.1080/00207720010005636).
    27. 27)
      • 31. Chen, S.H., Chou, J.H., Fong, I.K.: ‘Robust rank preservation of matrices with structured and unstructured uncertainties and its applications’, Proc. Inst. Mech. Eng. I, J. Syst. Control Eng., 2001, 215, pp. 499–504.
    28. 28)
      • 9. Chou, J.H.: ‘Pole-assignment robustness in a specified disk’, Syst. Control Lett., 1991, 16, pp. 41–44 (doi: 10.1016/0167-6911(91)90027-C).
    29. 29)
      • 27. Desoer, C.A., Vidyasagar, M.: ‘Feedback systems: input-output properties’ (Academic Press, New York, 1975).
    30. 30)
      • 30. Ortega, J.M.: ‘Numerical analysis’ (Academic Press, New York, 1972).
    31. 31)
      • 17. Duan, G.R., Yu, H.H.: ‘Robust pole assignment in high-order descriptor linear systems via proportional plus derivative state feedback’, IET Control Theory Appl., 2008, 2, pp. 277–287 (doi: 10.1049/iet-cta:20070164).
    32. 32)
      • 18. Liu, T.K., Chen, S.H., Chou, J.H., Chen, C.Y.: ‘Regional eigenvalue-clustering robustness of linear uncertain multivariable output feedback PID control systems’, J. Franklin Inst., 2009, 346, pp. 253–266 (doi: 10.1016/j.jfranklin.2008.09.001).
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