Journal of Advanced Navigation Technology (한국항행학회논문지)

The Korean Navigation Institute (한국항행학회)
권호 표지
DOI QR코드

DOI QR Code

Stability Condition of Discrete System with Time-varying Delay and Unstructured Uncertainty

비구조화된 불확실성과 시변 지연을 갖는 이산 시스템의 안정 조건

  • Han, Hyung-seok (Department of Electronic Engineering, Gachon University)
  • 한형석 (가천대학교 전자공학과)
  • Received : 2018.10.16
  • Accepted : 2018.12.11
  • Published : 2018.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we consider the stability condition for the linear discrete systems with time-varying delay and unstructured uncertainty. The considered system has time invariant system matrices for non-delayed and delayed state variables, but its delay time is time-varying within certain interval and it is subjected to nonlinear unstructured uncertainty which only gives information on uncertainty magnitude. In the many previous literatures, the time-varying delay and unstructured uncertainty can not be dealt in simultaneously but separately. In the paper, new stability conditions are derived for the case to which two factors are subjected together and compared with the existing results considering only one factor. The new stability conditions improving many previous results are proposed as very effective inequality equations without complex numerical algorithms such as LMI(Linear Matrix Inequality) or Lyapunov equation. By numerical examples, it is shown that the proposed conditions are able to include the many existing results and have better performances in the aspects of expandability and effectiveness.

본 논문에서는 시변 지연이 있는 선형 이산 시스템에 비구조화된 불확실성이 존재하는 경우에 대하여 시스템의 안정성을 다룬다. 고려된 시스템은 지연 없는 상태변수와 지연 상태 변수에 대한 시스템 행렬들은 시불변이나 지연시간이 구간범위에서 시변으로 변동하고, 크기에 대한 정보만을 얻을 수 있는 비구조화된 비선형 불확실성이 있는 시스템이다. 기존의 많은 결과들은 시변지연과 비구조화된 불확실성을 동시에 고려하지 못하고 한 가지 요소만 고려하여 연구되었다. 본 논문에서는 이 두 가지 요소를 모두 고려하여 새로운 안정조건을 도출하였고, 한 가지 요소만 고려한 기존 연구 결과와 비교하였다. 새로운 안정조건은 기존의 결과를 포함하는 매우 효과적인 수식으로 제안되며, 이는 복잡한 선형행렬부등식 혹은 리아프노프 방정식 등과 같은 복잡한 수치계산을 요구하지 않는 간단한 부등식이다. 수치예제를 통하여 제안된 안정조건이 기존의 결과들을 포함할 수 있음을 보이고 확장성과 효용성이 우수함을 확인한다.

Keywords

References

  1. D. L. Debeljkovic, and S. Stojanovic, "The stability of linear discrete time delay systems in the sense of Lyapunov: an overview," Scientific Technical Review, Vol. 60, No. 3, pp. 67-81, Mar. 2010.
  2. P. G. Park, W. I. Lee, and S. Y. Lee, "Stability on time delay systems: A survey," Journal of Institute of Control, Robotics and Systems, Vol. 20, No. 3, pp. 289-297, Mar. 2014. https://doi.org/10.5302/J.ICROS.2014.14.9016
  3. S. Xu, J. Lam, B. Zhang and Y. Zou, "A new result on the delay-dependent stability of discrete systems with time-varying delays," International Journal of Robust and Nonlinear Control, Vol. 24, No. 16, pp. 2512-2521, Oct. 2014. https://doi.org/10.1002/rnc.3006
  4. L. V. Hien, and H. Trinh, "New finite-sum inequalities with applications to stability of discrete time-delay systems," Automatica, Vol. 71, pp. 197-201, Sep. 2016. https://doi.org/10.1016/j.automatica.2016.04.049
  5. C. H. Lee, "Sufficient conditions for robust stability of discrete large-scale interval systems with multiple time delays," Journal of Applied Mathematics and Physics, Vol. 5, No. 4, pp. 759-765, Apr. 2017. https://doi.org/10.4236/jamp.2017.54064
  6. H. S. Han, "New stability conditions for networked control system with time-varying delay time," Journal of Korea Navigation Institute, Vol. 17, No. 6, pp. 679-686, Dec. 2013.
  7. H. S. Han, "Stability condition for discrete interval time-varying system with time-varying delay time," Journal of Advanced Navigation Technology, Vol. 20, No. 5, pp. 475-481, Oct. 2016. https://doi.org/10.12673/jant.2016.20.5.475
  8. C. H. Lee, T. L. Hsien, and C. Y. Chen, "Robust stability of discrete uncertain time-delay systems by using a solution bound of the Lyapunov equation," Innovative Computing Information and Control Express Letters, Vol. 8, No. 5, pp. 1547-1552, May 2011.
  9. C. H. Lee and C. Y. Chen, "Robust stability analysis of discrete time-delay systems subjected to nonlinear uncertainties," in 5th International Conference on Biomedical Engineering and Informatics (BMEI 2012), Chongqing: China, pp. 1245-1249, Oct. 2012.
  10. S. B. Stojanovic and D. Debeljkovic, "Delay-dependent stability analysis for discrete-time systems with time varying state delay," Chemical Industry & Chemical Engineering Quaterly, Vol. 17, No. 4, pp. 497-503, Apr. 2011. https://doi.org/10.2298/CICEQ110621035S
  11. M. A. Jordan, Discrete Time Systems, 1st ed. London, UK: IntechOpen Limited, pp. 334, 2011.
  12. C. S. Zhou and J. L. Deng, "Stability analysis of grey discrete-time systems," IEEE Transactions on Automatic Control, Vol. 34, No. 2, pp. 173-175, Feb. 1989. https://doi.org/10.1109/9.21090

Cited by

  1. 비구조화 불확실성을 갖는 양의 시변 이산 구간 시스템의 안정 조건 vol.23, pp.6, 2018, https://doi.org/10.12673/jant.2019.23.6.577
  2. 비구조화된 불확실성을 갖는 이산 지연 시스템의 새로운 안정조건 vol.24, pp.6, 2020, https://doi.org/10.12673/jant.2020.24.6.607