Skip to main content
SpringerLink
Log in

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

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

  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)

  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)

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  15. A. Rachid, Some conditions on zeros to avoid step-response extrema. IEEE Trans. Autom. Control 40(8), 1501–1503 (1995)

    Article  MathSciNet  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, Beijing, 100191, China

    Huanchao Du, Xiaoguang Hu & Chaoqun Ma

Authors
  1. Huanchao Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoguang Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chaoqun Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huanchao Du.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Du, H., Hu, X. & Ma, C. A Technique for Determining Whether a Linear System has a Nondecreasing Step Response. Circuits Syst Signal Process 38, 5908–5919 (2019). https://doi.org/10.1007/s00034-019-01166-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-019-01166-2

Keywords

Search

Navigation