Exponential stability of singularly perturbed discrete systems with time-delay

International Journal of Innovative Computing, Information and Control

Volumn 9, Issue 2, 2013, Pages 865-874

  Park, Kyun Sang ^a   Lim, Jong Tae ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

Discrete time system; Singularly perturbed system; Time delay

Indexed keywords

COMPOSITE LYAPUNOV FUNCTIONS; DISCRETE TIME SYSTEM; EXPONENTIALLY STABLE; FREQUENCY-DOMAIN APPROACH; LYAPUNOV'S DIRECT METHOD; SINGULARLY PERTURBED DISCRETE SYSTEMS; SINGULARLY PERTURBED SYSTEMS; SUFFICIENT CONDITIONS;

ASYMPTOTIC STABILITY; DECAY (ORGANIC); DIGITAL CONTROL SYSTEMS; DISCRETE TIME CONTROL SYSTEMS; FREQUENCY DOMAIN ANALYSIS; LYAPUNOV FUNCTIONS; TIME DELAY;

PERTURBATION TECHNIQUES;

EID: 84877819196     PISSN: 13494198     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. P. V. Kokotovic, H. K. Khalil and J. O'Reilly, Singular Perturbation Method in Control: Analysis and Design, Academic, Orlando, 1986.
2. D. S. Naidu, Singular Perturbation Methodology in Control Systems, Peter Peregrinus, London, 1988.
3. H. K. Khalil, Nonlinear Systems, Prentice Hall, Upper Saddle River, NJ, 2002.
4. J. W. Wu and K.-S. Hong, Delay-independent exponential stability criteria for time-varying discrete delay systems, IEEE Trans. Autom. Control, vol.39, no.4, pp.811-814, 1994.
5. S.-I. Niculescu, Delay Effects on Stability: A Robust Control Approach, Springer, New York, 2001.
6. H. Gao and T. Chen, New results on stability of discrete-time systems with time-varying state delay, IEEE Trans. Autom. Control, vol.52, no.2, pp.328-334, 2007.
7. H. Kando and T. Iwazumi, Stabilizing feedback controllers for singularly perturbed discrete systems, IEEE Trans. Syst., Man, Cybern., vol.14, no.6, pp.903-911, 1984.
8. W. S. Kafri and E. H. Abed, Stability analysis of discrete-time singularly perturbed systems, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol.43, no.10, pp.848-850, 1996.
9. T.-H. S. Li, J.-S. Chiou and F.-C. Kung, Stability bounds of singularly perturbed discrete systems, IEEE Trans. Autom. Control, vol.44, no.10, pp.1934-1938, 1999.
10. F. Sun, Y. Hu and H. Liu, Stability analysis and robust controller design for uncertain discrete-time singularly perturbed systems, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, vol.12, no.5-6, pp.849-865, 2005.
11. P. Mei, J. Fu, Y. Gong and Z. Zhang, Generalized H2 control for fast sampling discrete-time fuzzy singularly perturbed systems, ICIC Express Letters, vol.5, no.4(B), pp.1487-1493, 2011.
12. H. Trinh and M. Aldeen, Robust stability of singularly perturbed discrete-delay systems, IEEE Trans. Autom. Control, vol.40, no.9, pp.1620-1623, 1995.
13. C. F. Chen, S. T. Pan and J. G. Hsieh, Stability analysis for a class of uncertain discrete singularly perturbed systems with multiple time delays, ASME Journal of Dynamic Systems, Measurement, and Control, vol.124, pp.467-472, 2002.
14. J.-S. Chiou, Stability bound of discrete multiple time-delay singularly perturbed systems, Int. J. Syst. Sci., vol.37, no.14, pp.1069-1076, 2006.
15. F.-H. Hsiao, J.-D. Hwang and S.-T. Pan, D-stability problem of discrete singularly perturbed systems, Int. J. Syst. Sci., vol.34, no.3, pp.227-236, 2003.
16. S. T. Pan, The order reduction and robust D-stability analysis of discrete uncertain time-delay systems by time-scale separation, Control and Cybernectics, vol.32, no.4, pp.743-760, 2004.
17. F.-H. Hsiao, S.-T. Pan and C.-C. Teng, An efficient algorithm for finding the D-stability bound of discrete singularly perturbed systems with multiple time delays, Int. J. Control, vol.72, no.1, pp.1-17, 1999.
18. R. Bouyekhf and A. E. Moudni, Stabilization and regulation of class of non-linear singularly perturbed discrete-time systems, J. Franklin Inst., vol.335B, no.5, pp.963-982, 1998.
19. R. Bouyekhf, A. E. Hami and A. E. Moudni, Optimal control of a particular class of singularly perturbed nonlinear discrete-time systems, IEEE Trans. Autom. Control, vol.46, no.7, pp.1097-1101, 2001.
20. K.-S. Park and J.-T. Lim, Stability analysis of nonstandard nonlinear singularly perturbed discrete systems, IEEE Trans. Circuits Syst. II, Exp. Briefs, vol.58, no.5, pp.309-313, 2011.