Browse > Article
http://dx.doi.org/10.12673/jant.2016.20.5.475

Stability Condition for Discrete Interval Time-varying System with Time-varying Delay Time  

Han, Hyung-seok (Department of Electronic Engineering, Gachon University)
Publication Information
Journal of Advanced Navigation Technology / v.20, no.5, 2016 , pp. 475-481 More about this Journal
Abstract
In this paper, the new stability condition of linear discrete interval time-varying systems with time-varying delay time is proposed. The considered system has interval time-varying system matrices for both non-delayed and delayed states with time-varying delay time within given interval values. The proposed condition is derived by using Lyapunov stability theory and expressed by very simple inequality. The restricted stability issue on the interval time-invariant system is expanded to interval time-varying system and a powerful stability condition which is more comprehensive than the previous is proposed. As a results, it is possible to avoid the introduction of complex linear matrix inequality (LMI) or upper solution bound of Lyapunov equation in the derivation of sufficient condition. Also, it is shown that the proposed result can include the many existing stability conditions in the previous literatures. A numerical example in the pe revious works is modified to more general interval system and shows the expandability and effectiveness of the new stability condition.
Keywords
Discrete interval time-varying system; Time-varying delay time; Sufficient condition; Stability;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
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 T. Mori, N. Fukuma and M. Kuwahara, "Delay-independent stability criteria for discrete-delay systems," IEEE Transactions on Automatic Control, Vol. 27, No. 4, pp. 964-966, Aug. 1982.   DOI
3 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 (ICIC Express Letters), Vol. 8, No. 5, pp. 1547-1552, May 2011.
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.   DOI
5 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.   DOI
6 O. M. Kwon, M. J. Park, J. H. Park, S.M .Lee, and E. J. Cha, "Stability and stabilization for discrete-time systems with time-varying delays via augmented Lyapunov-Krasovskii functional," Journal of the Franklin Institute, Vol. 350, No. 3, pp. 521-540, Apr. 2013.   DOI
7 Z. Zuon, and H. L. Y.Wang, "New criterion for finite-time stability of linear discrete-time systems with time-varying delay," Journal of the Franklin Institute, Vol. 350, No. 9, pp. 2745-2756, Nov. 2013.   DOI
8 K. Ramakrishnan, and G. Ray, "Robust stability criteria for a class of uncertain discrete-time systems with time-varying delay," Applied Mathematical Modelling, Vol. 37, No. 3, pp. 1468-1479, Feb. 2013.   DOI
9 S. B. Stojanovic, D. L. J. Debeljkovic and N. Dimitrijevic, "Stability of discrete-time systems with time-varying delay: delay decomposition approach," International Journal of Computers Communications & Control, Vol. 7, No. 4 , pp. 776-784, Nov. 2012.
10 C. Y. Kao, "On stability of discrete-time LTI systems with varying time delays," IEEE Transactions on Automatic Control, Vol. 57, No. 5, pp. 1243-1248, May 2012.   DOI
11 M. Buslowicz and T. Kaczorek, "Robust stability of positive discrete-time interval systems with time-delays," Bulletin of The Polish Academy of Sciences Technical Sciences, Vol. 52, No. 2, pp. 99-102, Feb. 2004.
12 M. Buslowicz, "Simple stability conditions for linear positive discrete-time systems with delays," Bulletin of The Polish Academy of Sciences Technical Sciences, Vol. 56, No. 4, pp. 325-328, Apr. 2008.
13 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.
14 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.   DOI
15 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.
16 R. A. Hornand, and C. R. Johnson, Matrix Analysis, Cambridge, UK: Cambridge University Press, pp. 491, 1985.
17 H. S. Han and D. L. Lee, "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.