Robust H∞ filtering of Markovian jump stochastic systems with uncertain transition probabilities

International Journal of Systems Science

Volumn 42, Issue 7, 2011, Pages 1219-1230

  Yao, Xiuming ^a,b   Wu, Ligang ^a   Zheng, Wei Xing ^c   Wang, Changhong ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b NORTH CHINA ELECTRIC POWER UNIVERSITY   (China)

^c UNIVERSITY OF WESTERN SYDNEY   (Australia)

Author keywords

H filtering; Markovian jump systems; stochastic systems; time varying delay; uncertain transition probability

Indexed keywords

ADMISSIBLE PARAMETERS; ATTENUATION LEVELS; FILTERING ERROR; FREE-WEIGHTING MATRICES; LYAPUNOV-KRASOVSKII FUNCTIONALS; MARKOVIAN JUMP SYSTEMS; MARKOVIAN JUMPS; MARKOVIAN STOCHASTIC SYSTEMS; MODE TRANSITIONS; NUMERICAL EXAMPLE; NUMERICAL SOFTWARE; ROBUST H; STOCHASTIC DISTURBANCES; SUFFICIENT CONDITIONS; SYSTEM MATRICES; TIME-VARYING DELAY; TRANSITION PROBABILITIES;

DISTURBANCE REJECTION; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; TELECOMMUNICATION NETWORKS; TIME VARYING CONTROL SYSTEMS;

STOCHASTIC SYSTEMS;

EID: 79959555276     PISSN: 00207721     EISSN: 14645319     Source Type: Journal    
DOI: 10.1080/00207720903513350     Document Type: Article

References (39)

1. Basin, M., and Calderon-Alvarez, D. (2008), 'Alternative Optimal Filter for Linear Systems with Multiple State and Observation Delays', International Journal of Innovative Computing Information and Control, 4, 2889-2898.
2. Boukas, E.K. (2009), 'ℋ ∞ Control of Discrete-time Markov Jump Systems with Bounded Transition Probabilities', Optimal Control Application Methods, 30, 477-494.
3. Cao, Y., and Lam, J. (2000), 'Robust 'ℋ ∞ Control of Uncertain Markovian Jump Systems with Time Delay', IEEE Transactions on Automatic Control, 45, 77-83. (Pubitemid 30581599)
4. de Souza, C.E., and Fragoso, M.D. (2002), ''ℋ ∞ Filtering for Markovian Jump Linear Systems', International Journal of Systems Science, 33, 909-915.
5. de Souza, C.E., Trofino, A., and Barbosa, K.A. (2006), 'Mode-independent 'ℋ ∞Filters for Markovian Jump Linear Systems', IEEE Transactions on Automatic Control, 51, 1837-1841. (Pubitemid 44824371)
6. Feng, J., Lam, J., Xu, S., and Shu, Z. (2008), 'Stabilisation of Stochastic Systems with Optimal Decay Rate', IET ControlTheory & Applications, 2, 1-6. (Pubitemid 351169603)
7. Gao, H., Meng, X., and Chen, T. (2008), 'A Parameterdependent Approach to Robust 'ℋ ∞ Filtering for Time-delay Systems', IEEE Transactions on Automatic Control, 53, 2420-2425.
8. 2-ℒ1 Filtering for a Class of Uncertain Nonlinear Time-delay Systems', IEEE Transactions on Automatic Control, 48, 1661-1666.
9. Gao, H., and Wang, C. (2004), 'A Delay-dependent Approach to Robust 'ℋ ∞ Filtering for Uncertain Discrete-time State-delayed Systems', IEEE Transactions on Signal Processing, 52, 1631-1640.
10. Garcia, M., Basin, M.V., and Sanchez, Y. (2009), 'Risksensitive Approach to Optimal Filtering and Control for Linear Stochastic Systems', International Journal of Innovative Computing Information and Control, 5, 1599-1614.
11. Higham, D. (2001), 'An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations', SIAM Review, 43, 525-546. (Pubitemid 32991214)
12. Hu, L., Shi, P., and Frank, P.M. (2006), 'Robust Sampleddata Control for Markovian Jump Linear Systems', Automatica, 42, 2025-2030. (Pubitemid 44436049)
13. Hu, K., and Yuan, J. (2009), 'Improved Robust 'ℋ ∞ Filtering for Uncertain Discrete-time Switched Systems', IET Control Theory & Applications, 3, 315-324.
14. Karan, M., Shi, P., and Kaya, C.Y. (2006), 'Transition Probability Bounds for the Stochastic Stability Robustness of Continuous- and Discrete-time Markovian Jump Linear Systems', Automatica, 42, 2159-2168. (Pubitemid 44647194)
15. Liu, Y., and Wang, W. (2009), 'Fuzzy 'ℋ ∞ Filtering for Nonlinear Stochastic Systems with Missing Measurements', ICIC Express Letters, 3, 739-744.
16. Ma, S., and Boukas, E.K. (2009), 'Robust 'ℋ ∞ Filtering for Uncertain Discrete Markov Jump Singular Systems with Mode-dependent Time-delay', IET Control Theory & Applications, 3, 351-361.
17. Nguang, S.K., Assawinchaichote, W., and Shi, P. (2007), 'Robust 'ℋ ∞ Control Design for Fuzzy Singularly Perturbed Systems with Markovian Jumps: An LMI Approach', IET Control Theory & Applications, 1, 893-908. (Pubitemid 46990244)
18. Niu, Y., and Ho, D.W.C. (2006), 'Robust Observer Design for Itô Stochastic Time-delay Systems via Sliding Mode Control', Systems & Control Letters, 55, 781-793. (Pubitemid 44067267)
19. Niu, Y., Ho, D.W.C., and Lam, J. (2005), 'Robust Integral Sliding Mode Control for Uncertain Stochastic Systems with Time-varying Delay', Automatica, 41, 873-880. (Pubitemid 40352401)
20. Niu, Y., Ho, D.W.C., and Wang, X. (2007), 'Sliding Mode Control for Itô Stochastic Systems with Markovian Switching', Automatica, 43, 1784-1790. (Pubitemid 47374629)
21. Shi, P., Boukas, E.K., and Agarwal, R.K. (1999), 'Control of Markovian Jump Discrete-time Systems with Norm Bounded Uncertainty and Unknown Delay', IEEE Transactions on Automatic Control, 44, 2139-2144. (Pubitemid 30531659)
22. Shi, P., Mahmoud, M., Nguang, S., and Ismail, A. (2006), 'Robust Filtering for Jumping Systems with Modedependent Delays', Signal Processing, 86, 140-152. (Pubitemid 41681311)
23. Shi, P., Xia, Y., Liu, G., and Rees, D. (2006), 'On Designing of Sliding-mode Control for Stochastic Jump Systems', IEEE Transactions on Automatic Control, 51, 97-103. (Pubitemid 43137935)
24. Sun, M., Lam, J., Xu, S., and Zou, Y. (2007), 'Robust Exponential Stabilization for Markovian Jump Systems With mode-dependent Input Delay', Automatica, 43, 1799-1807. (Pubitemid 47374638)
25. Wang, Z., Lam, J., and Liu, X. (2004), 'Robust Filtering For discrete-time Markovian Jump Delay Systems', IEEE Signal Processing Letters, 11, 659-662.
26. Wang, Z., Liu, Y., and Liu, X. (2008), 'ℋ ∞ Filtering for Uncertain Stochastic Time-delay Systems with Sectorbounded nonlinearities', Automatica, 44, 1268-1277.
27. Wang, Z., Qiao, H., and Burnham, K.J. (2002), 'On Stabilization of Bilinear Uncertain Time-delay Stochastic Systems with Markovian Jumping Parameters', IEEE Transactions on Automatic Control, 47, 640-646. (Pubitemid 34554833)
28. Wang, Y., Xie, L., and de Souza, C.E. (1992), 'Robust Control of a Class of Uncertain Nonlinear System', Systems & Control Letters, 19, 139-149. (Pubitemid 23572546)
29. Wei, G., Wang, Z., Shu, H., and Fang, J. (2006), 'Robust ℋ ∞ Control of Stochastic Time-delay Jumping Systems with Nonlinear Disturbances', Optimal Control Application and Methods, 27, 255-271. (Pubitemid 44662015)
30. Wei, G., Wang, Z., Shu, H., and Fang, J. (2007), 'A Delaydependent Approach to ℋ ∞ Filtering for Stochastic Delayed Jumping Systems with Sensor Non-linearities', International Journal of Control, 80, 885-897.
31. Wu, L., Shi, P., Gao, H., and Wang, C. (2006), 'Delaydependent Robust ℋ ∞ and ℒ2-ℒ1 Filtering for LPV Systems with Both Discrete and Distributed Delays', IET Control Theory & Applications, 153, 483-492. (Pubitemid 43781903)
32. Wu, L., Shi, P., Gao, H., and Wang, C. (2008), 'ℋ ∞ Filtering for 2D Markovian Jump Systems', Automatica, 44, 1849-1858.
33. Xia, Y., Zhu, Z., and Mahmoud, M.S. (2009), 'ℋ2 Control for Networked Control Systems with Markovian Data Losses and Delays', ICIC Express Letters, 3, 271-276.
34. Xiong, J., and Lam, J. (2006), 'Stabilization of Discrete-time Markovian Jump Linear Systems via Time-delayed Controllers', Automatica, 42, 747-753.
35. Xiong, J., Lam, J., Gao, H., and Ho, D.W.C. (2005), 'On Robust Stabilization of Markovian Jump Systems with Uncertain Switching Probabilities', Automatica, 41, 897-903. (Pubitemid 40352404)
36. Xu, S., Chen, T., and Lam, J. (2003), 'Robust ℋ ∞ Filtering for Uncertain Markovian Jump Systems with Modedependent Time-delays', IEEE Transactions on Automatic Control, 48, 900-907.
37. Xu, S., Lam, J., and Mao, X. (2007), 'Delay-dependent ℋ ∞ Control and Filtering for Uncertain Markovian Jump Systems with Time-varying Delays', IEEE Transactions on Circuit and Systems I, 54, 2070-2077. (Pubitemid 47456047)
38. Zhang, L., Boukas, E.K., and Lam, J. (2008), 'Analysis and Synthesis of Markov Jump Linear Systems with Timevarying Delays and Partially Known Transition Probabilities', IEEE Transactions on Automatic Control, 53, 2458-2464.
39. Zhong, M., Lam, J., Ding, S.X., and Shi, P. (2004), 'Robust Fault Detection of Markovian Jump Systems', Circuits Systems and Signal Processing, 23, 387-407.