Robust static output feedback control for stochastic hybrid systems

International Journal of Innovative Computing, Information and Control

Volumn 4, Issue 9, 2008, Pages 2295-2304

  Lin, Zhongwei ^a   Zhang, Weihai ^b   Lin, Yan ^a  

^a BEIHANG UNIVERSITY   (China)

^b SHANDONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Linear matrix inequality (LMI); Markovian jumps; Stabilization; Static output feedback control; Stochastic systems

Indexed keywords

EID: 63549123132     PISSN: 13494198     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. I. Y. Kats and N. N. Krasovskii, On the stability of systems with random parameters, Prikl. Mat. Mekh, vol. 27, pp. 809-823, 1960.
2. N. N. Krasovskii and E. A. Lidskii, Analytic design of controller in systems with random attributes, Aut. Remote Control I, II, III, vol. 22, pp. 1021-1025, 1141-1146, 1289-1294, 1961.
3. T. Basar, Minimax control of switching systems under sampling, Systems and Control Letters, vol. 25, pp. 315-325, 1995.
4. D. D. Sworder, Feedback control of a class of linear systems with jump parameters, IEEE Thins. Automat. Contr., vol. 14, pp. 9-14, 1969.
5. Y. Ji and H. J. Chizeck, Jump linear quadratic Gaussian control: Steady state solution and testable conditions, Control - Theory and Advanced Technology, vol. 6, pp. 289-319, 1990.
6. L. Xie, Output feedback H∞ control of systems with parameter uncertainty, Int. J. Contr., vol. 63, no. 4, pp. 741-750, 1996.
7. D. W. C. Ho and G. Lu, Robust stabilization for a class of discrete-time non-linear systems via output feedback: The unified LMI apprach, Int. J. Contr., vol. 76, no. 2, pp. 105-115, 2003.
8. M. Mariton, Jump Linear Systems in Automatic Control, Marcel Dekker, New York, 1990.
9. I. Y. Kats and N. N. Krasovskii, On the stability of systems with random parameters, Prikl. Mat. Mekh, vol. 27, pp. 809-823, 1960.
10. P. Shi, E. K. Boukas and R. K. Agarwal, Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay, IEEE Trans. Automat. Contr, vol. 44, no. 11, pp. 2139-2144, 1999.
11. G. L. Ei and M. A. Rami, Robust state-feedback stabilization of jump linear systems via LMIs, Int. J. Robust and Nonlinear Control, vol. 6, pp. 1015-1022, 1996.
12. E. K. Boukas, Stochastic Hybrid Systems: Analysis and Design, Bostom: Birkhauser, 2005.
13. P. Shi and E. K. Boukas, H∞-control for Markovian jumping linear systems with parametric uncertainty, Journal of Optimization Theory and Applications, vol. 95, no. 1, pp. 75-99, 1997.
14. T. Bjork, Finite dimensional optimal filters for a class of Itô-processes with jumping parameters, Stochastics, vol. 4, pp. 167-183, 1980.
15. X. Li, X. Y. Zhou and M. A. Rami, Indefinite stochastic linear quadratic control with markovian jumps in infinite time horizon, Journal of Global Optimization Theory and Applications, vol. 27, pp. 149-175, 2003.
16. V. Blondel, M. Gevers and A. Lindquist, Survey on the state of systems and control, Eur. J. Control, vol. 1, pp. 5-23, 1995.
17. X. Mao, Stability of stochastic differential equations with Markovian switching, Stochastic Processes and their Applications, vol. 79, no. 1, pp. 45-67, 1999.
18. Z. Wang, H. Qiao and K. J. Burnham, On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters, IEEE Trans. Automat. Contr., vol. 47, no. 4, pp. 640-646, 2002.
19. D. Bernstein, Some open problems in matrix theory arising in linear systems and control, Linear Algebra Applications, vol. 162, no. 1, pp. 409-432, 1992.
20. V. Dragan and T. Morozan, The linear quadratic optimization problems for a class of linear stochastic systems with multiplicative white noise and Markovian jumping, IEEE Trans. Automat. Contr, vol. 49, no. 5, pp. 665-675, 2004.
21. V. L. Syrmos, C. T. Abdallah, P. Dorato and K. Grigoriadis, Static output feedback-A survey, Automatica, vol. 33, pp. 125-137, 1997.
22. E. K. Boukas, Static output feedback control for stochastic hybrid systems: LMI approach, Automatica, vol. 42, pp. 183-188, 2006.
23. P. V. Pakshin and D. M. Retinsky, Robust stabilization of jumping systems via static output feedback, Proc. of the Eur. Control Conf., Cambridge, 2003.
24. Y. Y. Cao, J. Lam and Y. X. Sun, Static output feedback stabilization: An ILMI approach, Automatic, vol. 34, no. 12, pp. 1641-1645, 1998.
25. Y. Wang and Z. Q. Sun, H∞ control of networked control system via LMI approach, International Journal of Innovative Computing, Information and Control, vol. 3, no. 2, pp. 343-352, 2007.
26. S. Aberkane, C. P. Jean and D. Sauter, Output feedback H∞ control of a class of stochastic hybrid systems with wiener process via convex analysis, International Journal of Innovative Computing, Information and Control, vol. 2, no. 6, pp. 1179-1196, 2006.