Skip to main content
Log in

Positive Sampled-Data Disturbance Attenuation: Separate Design

  • Original Article
  • Published:
Journal of Electrical Engineering & Technology Aims and scope Submit manuscript

Abstract

Robust positive sampled-data observer-based output-feedback energy-to-peak disturbance attenuation is challenging problem because of the following reasons. (i) The typical Luenberger observer has a limited structure for guaranteeing closed-loop positivity. (ii) The conventional sampled-data control framework has no lever to manage closed-loop positivity during sampling intervals and at sampling instants. (iii) A separation principle is to be established for this problem. In this paper, we propose an affirmative methodology to solve this problem.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

Notes

  1. We found that the state-space model introduced by Yin et al. [16] is uncontrollable and unobservable.

References

  1. Fridman E (2010) A refined input delay approach to sampled-data control. Automatica 46(2):421–427. https://doi.org/10.1016/j.automatica.2009.11.017

    Article  MathSciNet  Google Scholar 

  2. Haddad WM, Chellaboina V (2005) Stability and dissipativity theory for nonnegative dynamical systems: a unified analysis framework for biological and physiological systems. Nonlinear Anal Real World Appl 6(1):35–65. https://doi.org/10.1016/j.nonrwa.2004.01.006

    Article  MathSciNet  Google Scholar 

  3. Jee SC, Lee HJ (2022) Separation principle-based positive output-feedback \(l_{\infty }\)\(l_{\infty }\) disturbance attenuation. J Electr Eng Technol 17:3499–3505. https://doi.org/10.1007/s42835-022-01128-w

    Article  Google Scholar 

  4. Lee HJ (2022) Robust static output-feedback vaccination policy design for an uncertain SIR epidemic model with disturbances: positive Takagi–Sugeno model approach. Biomedical Signal Processing and Control 72:103273. https://doi.org/10.1016/j.bspc.2021.103273

    Article  Google Scholar 

  5. Lee HJ (2023) Positivity and separation principle for observer-based output-feedback disturbance attenuation of uncertain discrete-time fuzzy models with immeasurable premise variables. J Franklin Inst 360(12):8486–8505. https://doi.org/10.1016/j.jfranklin.2023.03.047

    Article  MathSciNet  Google Scholar 

  6. Lee HJ (2023) Robust observer-based output-feedback control for epidemic models: Positive fuzzy model and separation principle approach. Appl Soft Comput 132:109802. https://doi.org/10.1016/j.asoc.2022.109802

    Article  Google Scholar 

  7. Lee J, Moon JH, Jee SC, Lee HJ (2021) Robust \(\mathcal{L} _{\infty }\)\(l_{\infty }\) sampled-data dynamic output-feedback control for uncertain linear time-invariant systems through descriptor redundancy. J Electr Eng Technol 16(2):1051–1058. https://doi.org/10.1007/s42835-020-00603-6

    Article  Google Scholar 

  8. Lee J, Moon JH, Lee HJ (2021) Continuous-time synthesizing robust sampled-data dynamic output-feedback controllers for uncertain nonlinear systems in Takagi–Sugeno form: A descriptor representation approach. Inf Sci 565:456–468. https://doi.org/10.1016/j.ins.2021.02.032

    Article  MathSciNet  Google Scholar 

  9. Lee J, Moon JH, Lee HJ (2021) Robust \(\mathcal{H} _{\infty }\) and \(\mathcal {L} _{\infty }\)\(\mathcal {L} _{\infty }\) sampled-data dynamic output-feedback control for nonlinear system in T–S form including singular perturbation. Int J Syst Sci 52(7):1315–1328. https://doi.org/10.1080/00207721.2020.1856448

    Article  ADS  Google Scholar 

  10. Liu L, Zhang J, Shao Y, Deng X (2020) Event-triggered control of positive switched systems based on linear programming. IET Control Theory Appl 14(1):145–155. https://doi.org/10.1049/iet-cta.2019.0606

    Article  MathSciNet  Google Scholar 

  11. Moon JH, Lee HJ (2021) Sampled-data control of underwater gliders: digital redesign approach. Int J Control. https://doi.org/10.1080/00207179.2019.1638969

    Article  MathSciNet  Google Scholar 

  12. Nam PT, Thuan LQ, Nguyen TN, Trinh H (2021) Comparison principle for positive time-delay systems: An extension and its application. J Franklin Inst 358(13):6818–6834. https://doi.org/10.1016/j.jfranklin.2021.07.013

    Article  MathSciNet  Google Scholar 

  13. Nguyen CM, Pathirana PN, Trinh H (2018) Robust observer-based control designs for discrete nonlinear systems with disturbances. Eur J Control 44:65–72. https://doi.org/10.1016/j.ejcon.2018.09.002

    Article  MathSciNet  Google Scholar 

  14. Shu Z, Lam J, Gao H, Du B, Wu L (2008) Positive observers and dynamic output-feedback controllers for interval positive linear systems. IEEE Trans Circuits Syst I Regul Pap 55(10):3209–3222. https://doi.org/10.1109/tcsi.2008.924116

    Article  MathSciNet  Google Scholar 

  15. Xie L (1996) Output feedback \({H}_{\infty }\) control of systems with parameter uncertainties. Int J Control 63(4):741–750. https://doi.org/10.1080/00207179608921866

    Article  Google Scholar 

  16. Yin OQ, Tomlinson B, Chow AH, Chow MS (2003) A modified two-portion absorption model to describe double-peak absorption profiles of ranitidine. Clin Pharmacokinet 42(2):179–192. https://doi.org/10.2165/00003088-200342020-00005

    Article  CAS  PubMed  Google Scholar 

  17. Zemouche A, Rajamani R, Kheloufi H, Bedouhene F (2017) Robust observer-based stabilization of Lipschitz nonlinear uncertain systems via LMIs - discussions and new design procedure. Int J Robust Nonlinear Control 27(11):1915–1939. https://doi.org/10.1002/rnc.3644

    Article  MathSciNet  Google Scholar 

  18. Zhang D, Du B (2022) Event-triggered controller design for positive T-S fuzzy systems with random time-delay. J Franklin Inst 359(15):7796–7817. https://doi.org/10.1016/j.jfranklin.2022.08.024

    Article  MathSciNet  Google Scholar 

  19. Zhang J, Feng G (2014) Event-driven observer-based output feedback control for linear systems. Automatica 50(7):1852–1859. https://doi.org/10.1016/j.automatica.2014.04.026

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by Inha University Research Grant.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ho Jae Lee.

Ethics declarations

Conflicts of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jee, S.C., Lee, H.J. Positive Sampled-Data Disturbance Attenuation: Separate Design. J. Electr. Eng. Technol. 19, 1807–1815 (2024). https://doi.org/10.1007/s42835-023-01637-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42835-023-01637-2

Keywords

Navigation