- Volume 19 Issue 6
The stability condition of linear discrete interval systems with a time-varying delay time is considered. The considered system has interval 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. Compared to previous results, the stability issue on the interval systems is expanded to time-varying delay. Furthermore, the new condition can imply the existing results on the time-invariant case and show the relation between interval time-varying delay time and stability of the system. The proposed condition can be applied to find the stability bound of the discrete interval system. Some numerical examples are given to show the effectiveness of the new condition and comparisons with the previously reported results are also presented.
Discrete interval system;Time-varying delay time;Sufficient condition;Stability
- 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, 1982. https://doi.org/10.1109/TAC.1982.1103030
- D. Debeljkovic and S.Stojanovic, “The stability of linear discrete time delay systems over a finite time interval: an overview,” Scientific Technical Review, Vol. 61, No. 1, pp. 46-55, 2011.
- D. Debeljkovic, “Further results on stability of linear discrete time delay systems,” Scientific Technical Review, Vol. 60, No. 2, pp. 48-59, 2010.
- J. Liu and J. Zhang, "Note on stability of discrete-time time-varying delay systems," IET Control Theory & Applications, Vol. 6, No. 2, p. 335, 2012. https://doi.org/10.1049/iet-cta.2011.0147
- S. Stojanovic, D. Debeljkovic and I. Mladenovic, “Simple exponential stability criteria of linear discrete time-delay systems,” Serbian Journal of Electrical Engineering, Vol. 5, No. 2, pp. 191-198, 2008. https://doi.org/10.2298/SJEE0802191S
- 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, 2011.
- 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, 2010.
- N. S. Rousan and K. Jordan, "Stability of square interval matrices for discrete time systems," Engineering of Journal of the Universityof Qatar,Vol.14, pp.127-135, 2001.
- C. H. Lee and T. L. Hsien, “New sufficient conditions for the stability of continuous and discrete time-delay interval systems,” Journal of Franklin Institute, Vol. 334B, No. 2, pp. 233-240, 1997.
- P. Liuy, “Stability of continuous and discrete time-delay grey systems,” International Journal of Systems Science, Vol. 32, No. 7, pp. 947-952, 2001. https://doi.org/10.1080/00207720010005636
- P. L. Liu and W.-J. Shyr, “Another sufficient condition for the stability of grey discrete-time systems,” Journal of the Franklin Institute, Vol. 342, No. 1, pp. 15-23, Jan. 2005. https://doi.org/10.1016/j.jfranklin.2004.07.008
- J. Fang Han, J. Qing Qiu and J. Hua Zhai, "Stability analysis for perturbed discrete dynamic interval systems with time delay," in Second International Conference on Innovative Computing, Information and Control (ICICIC 2007), Kumamoto: Japan, pp. 587-587, Sep. 2007.
- J. Fang Han, H. Zhu Tian and Z. Y. Meng, "Criteria for robust stability of discrete-time dynamic interval systems with multiple time-delays," in Proceedings of the Ninth International Conference on Machine Learning and Cybernetics, Qingdao: China, pp. 11-14, 2010.
- 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.
- R. A. Hornand and C. R. Johnson, Matrix Analysis, Cambridge, UK: Cambridge University Press, pp. 491, 1985.
- Z. Gajic and M. Lelic, Modern Control Systems Engineering, Upper Saddle River, NJ: Prentice-Hall, pp. 179-183, 1996.