A discrete-time approach to stability analysis of systems with aperiodic sample-and-hold devices

IEEE Transactions on Automatic Control

Volumn 54, Issue 10, 2009, Pages 2440-2445

  Fujioka, Hisaya ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

Matrix exponential; Networked control systems; Quadratic stability; Sampled data systems

Indexed keywords

DISCRETE TIME SYSTEM; DISCRETE-TIME; EMBEDDED CONTROL SYSTEMS; MATRIX EXPONENTIAL; NETWORKED CONTROL SYSTEMS; NUMERICAL EXAMPLE; QUADRATIC STABILITY; SAMPLE-AND-HOLD; SAMPLED-DATA FEEDBACK; SAMPLED-DATA SYSTEMS; SAMPLING INTERVAL; STABILITY ANALYSIS; TIME VARYING;

ADAPTIVE CONTROL SYSTEMS; CONTINUOUS TIME SYSTEMS; CONTROL SYSTEM ANALYSIS; DIGITAL CONTROL SYSTEMS; EMBEDDED SYSTEMS; FEEDBACK; FEEDBACK CONTROL; SAMPLED DATA CONTROL SYSTEMS; STABILITY; SYSTEM STABILITY;

CONTROL SYSTEM STABILITY;

EID: 70350339793     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2009.2029304     Document Type: Article

References (34)

1. T. Chen and B. Francis, Optimal Sampled-Data Control Systems. New York: Springer, 1995.
2. D. Hristu-Varsakelis and W. Levine, Eds., Handbook of Networked and Embedded Control Systems. Boston, MA: Birkhäuser, 2005.
3. J. Hespanha, P. Naghshtabrizi, and Y. Xu, "A survey of recent results in networked control systems," Proc. IEEE, vol. 95, no. 1, pp. 138-162, Jan. 2007.
4. G. Walsh, H. Ye, and L. Bushnell, "Stability analysis of networked control systems," in Proc. Amer. Control Conf., 1999, pp. 2876-2880.
5. W. Zhang, M. Branicky, and S. Phillips, "Stability of networked control systems," IEEE Control Syst. Mag., vol. 21, pp. 84-99, 2001.
6. W. Zhang and M. Branicky, "Stability of networked control systems with time-varying transmission period," in Proc. Conf. Commun., Contr. Comput., 2001, CD ROM.
7. E. Fridman, A. Seuret, and J. Richard, "Robust sampled-data stabilization of linear systems: An input delay approach," Automatica, vol. 40, pp. 1441-1446, 2004.
8. E. Fridman, U. Shaked, and V. Suplin, "Input/output delay approach to robust sampled-data H∞ control," Syst. Control Lett., vol. 54, pp. 271-282, 2005.
9. P. Naghshtabrizi and J. Hespanha, "Designing an observer-based controller for a network control system," in Proc. 44th IEEE Conf. Decision Control, Eur. Control Conf., 2005, pp. 848-853.
10. V. Suplin, E. Fridman, and U. Shaked, "Sampled-data H∞ control and filtering: Nonuniform uncertain sampling," Automatica, vol. 43, pp. 1072-1083, 2007.
11. P. Naghshtabrizi, J. Hespanha, and R. Teel, "On the robust stability and stabilization of sampled-data systems: A hybrid system aproach," in Proc. 45th IEEE Conf. Decision Control, 2006, pp. 4873-4878.
12. P. Naghshtabrizi, J. Hespanha, and A. Teel, "Stability of delay impulsive systems with application to networked control systems," in Proc. Amer. Control Conf., 2007, pp. 4899-4904.
13. L. Mirkin, "Some remarks on the use of time-varying delay to model sample-and-hold circuits," IEEE Trans. Autom. Control, vol. 52, no. 6, pp. 1109-1112, Jun. 2007.
14. H. Fujioka, "Stability analysis of systems with aperiodic sample-andhold devices," Automatica, vol. 45, pp. 771-775, 2009.
15. A. Sala, "Computer control under time-varying sampling period: An LMI gridding approach," Automatica, vol. 41, pp. 2077-2082, 2005.
16. G.Walsh, O. Beldiman, and L. Bushnell, "Asymptotic behavior of nonlinear networked control systems," IEEE Trans. Autom. Control, vol. 46, no. 7, pp. 1093-1097, Jul. 2001.
17. D. Carnevale, A. Teel, and D. Necasić, "ALyapunov proof of an improved maximum allowable transfer interval for networked control systems," IEEE Trans. Autom. Control, vol. 52, no. 5, pp. 892-897, May 2007.
18. M. Cloosterman, N. van deWouw,W. Heemels, and H. Nijmeijer, "Stabilization of networked control systems with large delays and packet dropouts," in Proc. Amer. Control Conf., 2008, pp. 4991-4996.
19. Y. Pan, H. Marquez, and T. Chen, "Remote stabilization of networked control systems with unknown time varying delays by LMI techniques," in Proc. 44th IEEE Conf. Decision Control, Eur. Control Conf., 2005, pp. 1589-1594.
20. L. Hetel, J. Daafouz, and C. Iung, "Stabilization of arbitrary switched linear systems with unknown time-varying delays," IEEE Trans. Autom. Control, vol. 51, no. 10, pp. 1668-1674, Oct. 2006.
21. P. Khargonekar, I. Petersen, and K. Zhou,"Robust stabilization of uncertain linear systems: Quadratic stabilizability and.. control theory," IEEE Trans. Autom. Control, vol. 35, no. 3, pp. 356-361, Mar. 1990.
22. C. V. Loan, "The sensitivity of the matrix exponential," SIAM J. Numer. Anal., vol. 14, pp. 971-981, 1977.
23. B. Kågström, "Bounds and perturbation bounds for the matrix exponential," BIT, vol. 17, pp. 89-97, 1977.
24. A. Balluchi, P. Murrieri, and A. Sangiovanni-Vincentelli, "Controller synthesis on non-uniform and uncertain discrete-time domains," in Hybrid Systems: Computation and Control. New York: Springer, 2005.
25. L. Hetel, J. Daafouz, and C. Iung, "Analysis and control of LTI and switched systems in digital loops via an event-based modelling," Int. J. Control, vol. 81, pp. 1125-1138, 2008.
26. H. Fujioka, "Stability analysis for a class of networked/embedded control systems: A discrete-time approach," in Proc. Amer. Control Conf., 2008, pp. 4997-5002.
27. J. Löfberg, "YALMIP: A toolbox for modeling and optimization in MATLAB," in Proc. IEEE CACSD Conf., 2004, pp. 284-289.
28. R. Tutuncu, K. Toh, and M. Todd, "Solving semidefinite-quadratic-linear programs using SDPT3," Math. Programming Ser. B, vol. 95, pp. 189-217, 2003.
29. A. Megretski and A. Rantzer, "System analysis via integral quadratic constraints," IEEE Trans. Autom. Control, vol. 42, no. 6, pp. 819-830, Jun. 1997.
30. T. Iwasaki and S. Hara, "Well-posedness of feedback systems: Insights into exact robustness analysis and approximate computations," IEEE Trans. Autom. Control, vol. 48, no. 5, pp. 619-630, May 1998.
31. H. Fujioka, "Stability analysis for a class of networked/embedded control systems: Output feedback case," in Proc. 17th IFAC World Congress, 2008, pp. 4210-4215.
32. H. Fujioka and T. Nakai, "Stabilizing systems with aperiodic sample-and-hold devices," in Proc. UKACC Int. Conf. Control, 2008, CD ROM.
33. Y. Suh, "Stability and stabilization of nonuniform sampling systems," Automatica, vol. 44, pp. 3222-3226, 2008.
34. J. Skaf and S. Boyd, "Analysis and synthesis of state-feedback controllers with timing jitter," IEEE Trans. Autom. Control, vol. 54, no. 3, pp. 652-657, Mar. 2009.