Journal of Control Theory and Applications

, Volume 2, Issue 1, pp 85–88 | Cite as

On the order of stable compensators for a class of time-delay system

  • Hanlin He
  • Zhongsheng Wang
  • Xiaoxin Liao
Brief Paper
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Accepted:

Abstract

The stabilization using a stable compensator does not introduce additional unstable zeros into the closed-loop transfer function beyond those of the original plant, so it is a desirable compensator, the price is that the compensator’s order will go up. This note considered the order of stable compensators for a class of time-delay systems. First, it is shown that for single-loop plants with at most one real right-half plane zero, a special upper bound for the minimal order of a strongly stabilizing compensator can be obtained in terms of the plant order; Second, it is shown that approximate unstable pole-zero cancellation does not occur, and the distances between distinct unstable zeroes are bounded below by a positive constant, then it is possible to find an upper bound for the minimal order of a strongly stabilizing compensator.

Keywords

Stabilization Strong stabilization Time-delay system Interpolation 
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References

  1. [1]
    R. E. Bellman, K. L. Cooke, Differential-Difference Equations, Academic, New York, 1963.MATHGoogle Scholar
  2. [2]
    L. Dugard, E. I. Verriest (Eds), Stability and Control of Time-delay Systems, Springer-Verlag, Berlin, Germany, 1997.Google Scholar
  3. [3]
    M. Vidyasagar, Control System Synthesis: A Factorization Approach, MIT Press, Cambridge, MA, 1985.MATHGoogle Scholar
  4. [4]
    H. Glusing-Luerben, A behavioral approach to delay-differential systems, AIAM J Control and Optimization, Vol. 35, No. 2, pp. 480–499,1997.CrossRefGoogle Scholar
  5. [5]
    E. W. Kamen, P. P. Khargonekar, A. Tannenbaum, Proper stable Bezout factorizations and feedback control of linear time-delay systems, Int. J. Control, Vol.43, No.3, pp.837–857,1986.MATHCrossRefGoogle Scholar
  6. [6]
    C. Bonnet, J. R. Partington, Bezout factors and L1-optimal controllers for delay systems using a two-parameter compensator scheme, IEEE Trans, on Automatic Control, Vol.44, No. 8, pp. 1512–1521,1999.MATHCrossRefGoogle Scholar
  7. [7]
    D. C. Youla, J. J. Jr Bongiorno, C. N. Lu, Single-loop feedback stabilization of linear multivariable plants, Automatica, Vol. 10, No. 1, pp.159–173,1974.MATHCrossRefGoogle Scholar
  8. [8]
    J. Q. Ying, Conditions for the strong stabilizabilities of n —D linear systems, Multidimensional System Signal Processing, Vol. 9, No. 1, pp. 125–148,1998.MATHCrossRefGoogle Scholar
  9. [9]
    Y. Y. Cao, J. Lam, On simultaneous H∞ control and strong H∞ stabilization, Automatica, Vol. 36, No. 6, pp. 859–865,2000.MATHCrossRefGoogle Scholar
  10. [10]
    M. Vidyasagar, N. Viswandham, Algebraic design techniques for reliable stabilization, IEEE Trans. on Automatic Control, Vol. 27, No. 10, pp.1085–1095,1982.MATHCrossRefGoogle Scholar
  11. [11]
    J. Q. Ying, Z. Lin, L. Xu, Some algebraic aspects of the strong stability of time-delay systems, IEEE Trans. on Automatic Control, Vol. 46, No.3, pp.454–457,2001.MATHCrossRefGoogle Scholar
  12. [12]
    M. C. Smith, K. P. Sondergeld, On the order of stable compensators, Automatica, Vol.22, No.l, pp. 127–129,1986.MATHCrossRefGoogle Scholar

Copyright information

© Journal of Control Theory and Application 2004

Authors and Affiliations

  • Hanlin He
    • 1
    • 2
  • Zhongsheng Wang
    • 1
  • Xiaoxin Liao
    • 1
  1. 1.Departmant of Control Science and EngineeringHuazhong University of Science and TechnologyWuhan HubeiChina
  2. 2.Culture and Science CollegeNaval University of EngineeringWuhan HubeiChina

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