- Volume 22 Issue 6
DOI QR Code
Stability Bound for Time-Varying Uncertainty of Positive Time-Varying Discrete Systems with Time-Varying Delay Time
시변 지연시간을 갖는 양의 시변 이산시스템의 시변 불확실성의 안정범위
- Han, Hyung-Seok (Dept. of Electronic Engr., Gachon University)
- 한형석 (가천대학교 전자공학과)
- Received : 2016.02.12
- Accepted : 2016.04.03
- Published : 2016.06.01
A simple new sufficient condition for asymptotic stability of the positive linear time-varying discrete-time systems, with unstructured time-varying uncertainty in delayed states, is established in this paper Compared with previous results that cannot be applied to time-varying systems; the time-varying system and delay time are considered simultaneously in this paper. The proposed conditions are compared with suitable conditions for the typical discrete-time systems. The considerations are illustrated by numerical examples of previous work.
- L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
- U. Krause, Positive Dynamical Systems in Discrete Time: Theory, Models, and Applications, Walter de Gruyter GmbH, Berlin/Munich/Boston, 2015.
- M. Buslowicz, "Simple conditions for robust stability of positive discrete-time linear systems with delays," Control and Cybernetics, vol. 39, no. 4, pp. 1159-1171, Apr. 2010.
- C. Zhang and Y. Sun, "Stability analysis of linear positive systems with time delays on time scales," Advances in Difference Equations, Open access, vol. 2012:56, 2012. https://doi.org/10.1186/1687-1847-2012-56
- 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.
- H. S. Han, "New stability conditions for positive time-varying discrete interval system with interval time-varying delay time," Journal of Advanced Navigation Technology (in Korean), vol. 17, no. 5, pp. 151-156, May 2014.
- 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 (in Korean), 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. LJ. 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.
- J. Liu and J. Zhang, "Note on stability of discrete-time time-varying delay systems," IET Control Theory & Applications, vol. 6, no. 2, pp. 335-339, Feb. 2012. https://doi.org/10.1049/iet-cta.2011.0147
- H. S. Han and D. H. Lee, "Stability bounds of delayed-time varying perturbations of discrete systems," Journal of Control, Automation, and Systems (in Korean), vol. 13, no. 2, pp. 147-153, Feb. 2007. https://doi.org/10.5302/J.ICROS.2007.13.2.147
- R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge, UK: Cambridge University Press, pp. 491, 1990.
- Z. Gajic and M. Lelic, Modern Control Systems Engineering, Upper Saddle River, NJ: Prentice-Hall, pp. 179-183, 1996.
- P. J. Antsaklis and A. N. Michel, Linear Systems, New York, NY: McGraw-Hill, pp. 500, 1998.
- 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.
- 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
- 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 (in Korean), vol. 20, no. 3, pp. 289-297, Mar. 2014. https://doi.org/10.5302/J.ICROS.2014.14.9016