Robust stabilizability of uncertain linear time-delay systems with markovian jumping parameters

Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

Volumn 118, Issue 4, 1996, Pages 776-783

  Benjelloun, K ^a   Boukas, E K ^a   Yang, H ^a  

^a ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001005626     PISSN: 00220434     EISSN: 15289028     Source Type: Journal    
DOI: 10.1115/1.2802356     Document Type: Article

References (31)

1. Barmish, B. R., Corless, M., and Leitmann, G., 1983, “A New Class of Stabilizing Controllers for Uncertain Dynamical Systems,” SIAM Journal of Control and Optimization, Vol. 21, No. 2, Mar.
2. Boukas, E. K., 1993, “Control of Systems with Controlled Jump Markov Disturbances,” Control Theory and Advanced Technology, Vol. 9, No. 2, June, pp. 577-595.
3. Boukas, E. K., and Haurie, A., 1990, “Manufacturing Flow Control and Preventive Maintenance: A Stochastic Control Approach,” IEEE Transactions on Automatic Control, AC-35 (9).
4. Boukas, E. K., 1996, Robust Linear Control: States Space Approach, forthcoming.
5. Boukas, E. K., and Yang, H., “Robust Stability of Nonlinear Piecewise Deterministic Systems under Matching Conditions,” 13th World Congress International Federation of Automatic Control, July 1-5, 1996.
6. Davis, M. H. A., 1984, “Piecewise-Deterministic Markov Processes: A General Class of Non-Diffusion Stochastic Models,” Journal. Royal Statistical Society, B46, pp. 353.
7. Cheres, E., Gutman, S., and Palmor, Z. J., 1989, “Stabilization of Uncertain Dynamic System Including State Delay,” IEEE Transactions on Automatic Control, Vol. 34, pp. 1199-1230.
8. Gregory J. Nazaroff, 1973, “Stability and Stabilization of Linear Differential Delay Systems,” IEEE Transactions on Automatic Control, pp. 317-318.
9. Gutman, S., 1979, “Uncertain Dynamical Systems—A Lyapunov Min-Max Approach,” IEEE Transactions on Automatic Control, Vol. 24, No. 3, pp. 437-443.
10. Ji, Y., and Chizek, H., 1990, “Controllability, Stabilizability, and ContinuousTime Markovian Jump Linear Quadratic Control,” IEEE Transactions on Automatic Control, Vol. 35, No. 7.
11. Ji, Y., Feng, X., Loparo, K. A., and Chizeck, H. J., 1992, “Stochastic Stability Properties of Jump Linear Systems,” IEEE Transactions on Automatic Control, Vol. 37, No. 1, pp. 38-53.
12. Kats, I. I., and Krasovskii, N. N., 1960, “On the Stability of Systems with Random Attributes,” Journal of Applied Mathematics and Mechanics, Vol. 24, pp. 1225-1246.
13. Khalil, H. K., 1992, Nonlinear Systems, Macmillan Publishing Company, New York.
14. Krasovskii, N. N., and Lidskii, E. A., 1961, “Analytical Design of Controllers in Systems with Random Attributes,” Automation and Remote Control, Parts I-III, No. 22, pp. 1021-1025.
15. Kreindler, E., and Jameson, A., 1972, “Conditions for Nonnegativeness of Partitioned Matrices,” IEEE Transactions on Automatic Control, Vol. AC-17, Feb., pp. 147-148.
16. Kushner, H. J., 1967, Stochastic Stability and Control, Academic, New York.
17. Leitmann, G., 1981, “On the Efficacy of Nonlinear Control in Uncertain Linear Systems,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 102, pp. 95-102.
18. Magdi, S. Mahmoud, and Naser, F. Al-Muthairi, 1994, “Design of Robust Controllers for Time-Delay Systems,” IEEE Transactions on Automatic Control, Vol. AC-39, No. 5, pp. 995-999.
19. Mariton, M., and Bertrand, P., 1985, “Output Feedback for a Class of Linear Systems with Stochastic Jump Parameters,” IEEE Transactions on Automatic Control, Vol. AC-30, No. 9, pp. 898-900.
20. Mariton, M., 1990, Jump Linear Systems in Automatic Control, New York and Basel.
21. Mori, T., Noldust, E., and Kuwahara, M., 1983, “A Way to Stabilize Linear Systems with Delayed State,” International Journal of Control, Vol. 19, pp. 571-573.
22. Mori, T., 1985, “Criteria for Asymptotic Stability of Linear Time-Delay Systems,” IEEE Transactions on Automatic Control, Vol. 30, 1985, pp. 158-161.
23. Rishel, R., 1975, “Control of System with Jump Markov Disturbances,” IEEE Transactions on Automatic Control, p. 241.
24. Su, Te-Jen, Kou, Te-Son, and York-Yih, Sun, 1988, “Robust Stability for Linear Time-Delay Systems with Linear Parameter Perturbation,” International Journal of Control, Vol. 19, No. 10, pp. 2123-2129.
25. Su, J. H., Fong, I-K., and Tseng, C. L., 1994, “Stability Analysis of Linear Systems with Time-Delay,” IEEE Transactions on Automatic Control, Vol. 39, No. 6, pp. 11341-1344.
26. Sworder, D., 1969, “Feedback Control of a Class of Linear Systems with Jump Parameters,” IEEE Transactions on Automatic Control, Vol. AC-14, pp. 9-14.
27. Thorp, J. S., and Barmish, B. R., 1981, “On Guaranteed Stability of Uncertain Linear Systems via Linear Control,” Journal of Optimization Theory and Application, Vol. 35, No. 4, pp. 559-579.
28. Trinh, H., and Aldeen, M., 1994, “Stabilization of Uncertain Dynamic Delay Systems by Memoryless Feedback Controllers,” International Journal of Control, Vol. 59, No. 6, pp. 1525-1542.
29. Vermes, D., 1985, “Optimal Control of Piecewise Deterministic Markov Process,” Stochastics, Vol. 14, p. 165.
30. Wang, S. S., Chen, B. S., and Lin, T. P., 1987, “Robust Stability of Uncertain Time-Delay Systems,” International Journal of Control, Vol. 46, No. 3, pp. 963-976.
31. Wonham, W. M., 1971, “Random Differential Equations in Control Theory,” Probabilistic Methods in Applied Mathematics, Vol. 2, A. T. Beruche-Reid, ed., N.Y.