Advertisement

Circuits, Systems, and Signal Processing

, Volume 38, Issue 12, pp 5908–5919 | Cite as

A Technique for Determining Whether a Linear System has a Nondecreasing Step Response

  • Huanchao DuEmail author
  • Xiaoguang Hu
  • Chaoqun Ma
Short Paper
  • 47 Downloads

Abstract

This paper deals with the problem of determining whether or not a linear system has a nondecreasing step response. Results are given in the form of root determination of a polynomial. These results can be applied to a more general class of systems, i.e., the system can be of arbitrary order, the zeros can be real or complex, and the poles of the system can be distributed arbitrarily along the negative real axis, including multiple poles.

Keywords

Nondecreasing step response Polynomial root determination Linear system Negative real poles 

Notes

References

  1. 1.
    A. Arbi, Dynamics of BAM neural networks with mixed delays and leakage time-varying delays in the weighted pseudo-almost periodic on time-space scales. Math. Methods Appl. Sci. 41(3), 1230–1255 (2018)MathSciNetCrossRefGoogle Scholar
  2. 2.
    A. Arbi, C. Aouiti, F. Cherif, A. Touati, A.M. Alimi, Stability analysis of delayed Hopfield neural networks with impulses via inequality techniques. Neurocomputing 158, 281–294 (2015)CrossRefGoogle Scholar
  3. 3.
    A. Arbi, J. Cao, Pseudo-almost periodic solution on time-space scales for a novel class of competitive neutral-type neural networks with mixed time-varying delays and leakage delays. Neural Process. Lett. 46(2), 719–745 (2017)CrossRefGoogle Scholar
  4. 4.
    A. Arbi, J. Cao, A. Alsaedi, Improved synchronization analysis of competitive neural networks with time-varying delays. Nonlinear Anal. Model. Control 23(1), 82–102 (2018)MathSciNetCrossRefGoogle Scholar
  5. 5.
    M. EI-Khoury, O.D. Crisalle, R. Longchamp, Influence of zero locations on the number of step-response extrema. Automatica 29(6), 1571–1574 (1993)MathSciNetCrossRefGoogle Scholar
  6. 6.
    S. Jayasuriya, A.G. Dharne, Necessary and sufficient conditions for nondecreasing step responses for LTI systems, Proceedings of the 2002 American Control Conference, Anchorage, AK, pp. 505–510 (2002)Google Scholar
  7. 7.
    S. Jayasuriya, M.A. Franchek, A class of transfer functions with non-negative impulse response. ASME J. Dyn. Syst. Meas. Control 113(2), 313–315 (1991)CrossRefGoogle Scholar
  8. 8.
    S. Jayasuriya, J.W. Song, On the synthesis of compensators for nondecreasing step response. ASME J. Dyn. Syst. Meas. Control 118(4), 757–763 (1996)CrossRefGoogle Scholar
  9. 9.
    X. Jiang, D. Gu, Z. Huang, T. Chen, On nondecreasing step responses of third-order SISO linear systems with a pair of complex poles, Proceedings of the American Control Conference, Arlington, VA, pp. 547–551 (2001)Google Scholar
  10. 10.
    H. Kobayashi, Output overshoot and pole-zero configuration, in Proceedings of the 12th IFAC World Congress. Automatic Control. Sydney, Australia, vol. 2, pp. 529–532 (1993)Google Scholar
  11. 11.
    Y. Liu, P.H. Bauer, Sufficient conditions for non-negative impulse response of arbitrary-order systems, in 2008 IEEE Asia Pacific Conference on Circuits and Systems, Macao, China, pp. 1410–1413 (2008)Google Scholar
  12. 12.
    S.K. Lin, C.J. Fang, The nonovershooting and nondecreasing step response of a third-order SISO linear system. IEEE Trans. Autom. Control 42, 1299–1303 (1997)MathSciNetCrossRefGoogle Scholar
  13. 13.
    J. Qiu, Y. Wei, H.R. Karimi, H. Gao, Reliable control of discrete-time piecewise-affine time-delay systems via output feedback. IEEE Trans. Reliab. 67(1), 79–91 (2018)CrossRefGoogle Scholar
  14. 14.
    J. Qiu, Y. Wei, L. Wu, A novel approach to reliable control of piecewise affine systems with actuator faults. IEEE Trans Circuits Syst II Express Briefs 64(8), 957–961 (2017)CrossRefGoogle Scholar
  15. 15.
    A. Rachid, Some conditions on zeros to avoid step-response extrema. IEEE Trans. Autom. Control 40(8), 1501–1503 (1995)MathSciNetCrossRefGoogle Scholar
  16. 16.
    A.H. Zemanian, Conditions on pole and zero locations which insure a nondecreasing step response. IRE Trans. Circuit Theory 6(1), 129–130 (1959)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Virtual Reality Technology and SystemsBeihang UniversityBeijingChina

Personalised recommendations