- Volume 21 Issue 6
DOI QR Code
Stability Bound for Time-Varying Uncertainty of Time-varying Discrete Interval System with Time-varying Delay Time
시변 지연시간을 갖는 이산 구간 시변 시스템의 시변 불확실성의 안정범위
- Han, Hyung-seok (Department of Electronic Engineering, Gachon University)
- 한형석 (가천대학교 전자공학과)
- Received : 2017.10.29
- Accepted : 2017.11.29
- Published : 2017.12.31
In this paper, we consider the stability bound for uncertainty of delayed state variables in the linear discrete interval time-varying systems with time-varying delay time. The considered system has an interval time-varying system matrix for non-delayed states and is perturbed by the unstructured time-varying uncertainty in delayed states with time-varying delay time within fixed interval. Compared to the previous results which are derived for time-invariant cases and can not be extended to time-varying cases, the new stability bound in this paper is applicable to time-varying systems in which every factors are considered as time-varying variables. The proposed result has no limitation in applicable systems and is very powerful in the aspects of feasibility compared to the previous. Furthermore. the new bound needs no complex numerical algorithms such as LMI(Linear Matrix Inequality) equation or upper solution bound of Lyapunov equation. By numerical examples, it is shown that the proposed bound is able to include the many existing results in the previous literatures and has better performances in the aspects of expandability and effectiveness.
- 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.
- 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
- 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
- M. N. A. Parlakci, "Robust stability of linear uncertain discrete-time systems with interval time-varying delay," Turkish Journal of Electrical Engineering & Computer Sciences, Vol. 22, No. 3, pp. 650- 662, Apr. 2014. https://doi.org/10.3906/elk-1209-119
- H. S. Han, "New stability conditions for positive time-varying discrete interval system with interval time-varying delay time," Journal of Korea Navigation Institute, Vol. 18, No. 5, pp. 501-507, Oct. 2014.
- H. S. Han, "Stability condition for discrete interval system with time-varying delay time," Journal of Korea Navigation Institute, Vol. 19, No. 6, pp. 574-580, Dec. 2015.
- 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
- H. S. Han, "Stability bound for time-varying uncertainty of positive time-varying discrete systems with time-varying delay time," Journal of Institute of Control, Robotics and Systems, Vol. 22, No. 6, pp. 424-428, Jun. 2016. https://doi.org/10.5302/J.ICROS.2016.16.0033
- H. S. Han, "Stability bounds of time-varying uncertainty and delay time for discrete systems with time-varying delayed state," Journal of Institute of Control, Robotics and Systems, Vol. 18, No. 10, pp. 895-901, Oct. 2012. https://doi.org/10.5302/J.ICROS.2012.18.10.895
- S. B. Stojanovic and D. L, J. Debeljkovic, "Further results on asymptotic stability of linear discrete time delay autonomous systems," International Journal of Information and Systems Sciences, Vol. 2, No. 1, pp. 117-123, Jan. 2006.
- H. S. Han and D. H. Lee, "Stability bounds of delayed-time varying perturbations of discrete systems," Journal of Control, Automation, and Systems, Vol. 13, No. 2, pp. 147-153, Feb. 2007. https://doi.org/10.5302/J.ICROS.2007.13.2.147
- R. A. Hornand, and C. R. Johnson, Matrix Analysis, Cambridge, UK: Cambridge University Press, pp. 491, 1985.
- 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