Mode-independent H∞ filters for Markovian jump linear systems

IEEE Transactions on Automatic Control

Volumn 51, Issue 11, 2006, Pages 1837-1841

  de Souza, Carlos E ^a   Trofino, Alexandre ^b   Barbosa, Karina A ^a  

^a LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

^b FEDERAL UNIVERSITY OF SANTA CATARINA   (Brazil)

Author keywords

H filtering; Markovian jump linear systems; Mode independent filter; Robust filtering

Indexed keywords

ASYMPTOTIC STABILITY; LYAPUNOV METHODS; MARKOV PROCESSES; ROBUSTNESS (CONTROL SYSTEMS); UNCERTAIN SYSTEMS;

LINEAR MATRIX INEQUALITIES; MARKOVIAN JUMP LINEAR SYSTEMS; MODE-INDEPENDENT FILTER;

LINEAR CONTROL SYSTEMS;

EID: 37849186947     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2006.883060     Document Type: Article

References (23)

1. 2 filtering for uncertain linear systems: LMI based methods with parameteric Lyapunov functions," Syst. Control Lett., vol. 54, pp. 251-262, 2005.
2. E. K. Boukas and Z. K. Liu, "Robust H∞ filtering for polytopic uncertain time-delay systems with Markov jumps," Comput. Electr. Eng., vol. 28, pp. 171-193, 2002.
3. E. D. F. Costa and J. B. R. do Val, "On the observability and detectability of continuous-time Markov jump linear systems," SIAM J. Control Optim., vol. 41, no. 4, pp. 1295-1314, 2002.
4. O. L. V. Costa, "Linear minimum mean square error estimation for discrete-time Markovian jump linear systems," IEEE Trans. Autom. Control, vol. 39, no. 8, pp. 1685-1689, Aug. 1994.
5. O. L. V. Costa and S. Guerra, "Robust linear filtering for discrete-time hybrid Markov linear systems," Int. J. Control, vol. 75, pp. 712-727, 2002.
6. C. E. de Souza, "A mode-independent H∞ filter design for discrete-time Markovian jump linear systems," in Proc. 42nd IEEE Conf. Decision Control, Maui, HI, Dec. 2003, pp. 2811-2816.
7. C. E. de Souza and M. D. Fragoso, "H∞ control for linear systems with Markovian jumping parameters," Control Theory Adv. Technol., vol. 9, pp. 457-466, 1993.
8. C. E. de Souza and M. D. Fragoso,, "H∞ filtering for Markovian jump linear systems," Int. J. Syst. Sci., vol. 33, pp. 909-915, 2002.
9. C. E. de Souza and M. D. Fragoso, "Robust filtering for uncertain Markovian jump linear systems," Int. J. Robust Nonlinear Control, vol. 12, pp. 435-446, 2002.
10. C. E. de Souza and M. D. Fragoso,, "H∞ filtering for discrete-time linear systems with Markovian jumping parameters," Int. J. Robust Nonlinear Control, vol. 13, pp. 1299-1316, 2003.
11. D. P. de Farias, J. C. Greomel, J. B. R. do Val, and O. L. V. Costa, "Output feedback control of Markov jump linear systems in continuous-time," IEEE Trans. Autom. Control, vol. 45, no. 5, pp. 944-949, May 2000.
12. X. Feng, K. A. Loparo, Y. Ji, and H. J. Chizeck, "Stochastic stability properties of jump linear systems," IEEE Trans. Autom. Control, vol. 37, no. 1, pp. 1884-1892, Jan. 1992.
13. M. D. Fragoso and J. Baczynski, "Optimal control for continuous-time linear quadratic problems with infinite Markov jump parameters," SIAM J. Control Optim., vol. 40, pp. 270-297, 2001.
14. M. D. Fragoso, O. L. V. Costa, and J. Baczynski, "The minimum linear mean square filter for a class of hybrid systems," in Proc. Eur. Control Conf., Porto, Portugal, Sep. 2001, pp. 319-323.
15. H. Liu, F. Sun, K. He, and Z. Sun, "Design of reduced-order H∞ filter for Markovian jumping systems with time delay," IEEE Trans. Circuits Syst. II, vol. 51, no. 11, pp. 607-612, Nov. 2004.
16. M. Mariton, Jump Linear Systems in Automatic Control. New York: Marcel Dekker, 1990.
17. K. M. Nagpal and P. P. Khargonekar, "Filtering and smoothing in an H∞ setting," IEEE Trans. Autom. Control, vol. 36, no. 2, pp. 152-166, Feb. 1991.
18. Z. Pan and T. Basar, "H∞ control of Markovian jump systems and solutions to associated piecewise-deterministic differential games," in Annals of the International Society of Dynamic Games, G. J. Olsder, Ed. Boston, MA: Birkhäuser, 1996, pp. 61-94.
19. U. Shaked, "H∞ minimum error state estimation of linear stationary processes," IEEE Trans. Autom. Control, vol. 35, no. 5, pp. 554-558, May 1990.
20. U. Shaked and Y. Theodor, "H∞-optimal estimation: A tutorial," in Proc. 31st IEEE Conf. Decision and Control, Tucson, AZ, Dec. 1992, pp. 2278-2286.
21. D. D. Sworder, "Feedback control for a class of linear systems with jump parameters," IEEE Trans. Autom. Control, vol. AC-14, no. 1, pp. 9-14, Feb. 1969.
22. W. H. Wonham, "Random differential equations in control theory," in Probabilistic Methods in Applied Mathematics, A. T. Bharucha-Reid, Ed. New York: Academic, 1970, vol. 2, pp. 131-212.
23. S. Xu, T. Chen, and J. Lan, "Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time-delays," IEEE Trans. Autom. Control, vol. 48, no. 5, pp. 900-907, May 2003.